# A new myth... or is it a truth?



## dbiegel (Oct 15, 2006)

I've noticed lately that there's a new "forum boner" myth of sorts emerging: that off-axis response should mirror on-axis response. It seems to have begun in the discussion of Patrick Bateman's awesome unity waveguide project...

So anyway, I'm not meaning to be a jerk or anything, but I guess I just don't get where this off axis should mirror on axis concept came from. Intuitively, it doesn't make sense to me and in fact goes against much of what I've researched, experienced, and experimented with in a car (though it makes some sense to me for a home or studio). Am I the only one who feels this way?

Maybe I'm just confused and I will certainly try to keep an open mind. I'd love it if someone could either explain to me the theory of why this is beneficial in a car, and/or point me to some white papers etc that back this theory up.


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## 14642 (May 19, 2008)

Considering off axis response in the design of a speaker system is definitely not a myth, but insisting that the off axis response should be *exactly the same* as on axis response isn't the best design goal, especially in a car where MUCH of the sound we hear is reflected. 

The link below is a good place to start, although it isn't an explanation of what happens in a car.

http://www.harman.com/wp/pdf/LoudspeakersandRoomsPt2.pdf

In a car it's sufficient to design a speaker system that won't have any obvious holes or peaks in the response due to drastically different speaker directivity at crossover points and then to equalize the response at the listening position (essentially the power response) so that it has some substantial bass boost, which is necessary in small rooms, and a high frequency response that falls gradually from about 1k up to 20k. With the exception of the bass boost, this curve looks like the power response of a speaker designed to sound good in rooms. 

It's the directivity index that describes this loudspeaker parameter. There's a much more in-depth explanation in Floyd Toole's recent book, "Sound Reproduction".


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## tspence73 (Oct 14, 2008)

Andy Wehmeyer said:


> Considering off axis response in the design of a speaker system is definitely not a myth, but insisting that the off axis response should be *exactly the same* as on axis response isn't the best design goal, especially in a car where MUCH of the sound we hear is reflected.


If anything, my common sense tells me that because the off-axis sound mixes very audibly with the on-axis sound in a car, I would think it would be VERY important to have them match up as much as possible in character. Heck, that seems even preferable in a larger room but probably not as critical because in a home environment you can put in acoustic paneling to eliminate the off-axis reflections. In a car you cannot totally remove reflections. You are forced to live with them and design around them.



> In a car it's sufficient to design a speaker system that won't have any obvious holes or peaks in the response due to drastically different speaker directivity at crossover points and then to equalize the response at the listening position (essentially the power response) so that it has some substantial bass boost, which is necessary in small rooms, and a high frequency response that falls gradually from about 1k up to 20k. With the exception of the bass boost, this curve looks like the power response of a speaker designed to sound good in rooms.
> 
> It's the directivity index that describes this loudspeaker parameter. There's a much more in-depth explanation in Floyd Toole's recent book, "Sound Reproduction".


I'm trying hard to go through your link and reference what you're saying here but I'm not able to draw a correlation between the audible off-axis reflections we are discussing and what you are saying here. I understand that even with poor off-axis reponse that a single position in the car can be EQ'd to sound correct but not likely for multiple seated positions.

From what I understand, the sound reflections inside a car is different from a home environment in that, a home environment has a longer delay with the reflections which causes the listener to sometimes interpret the room's reflection as a reflection (ambience) in the recording itself. In a car the reflections don't have enough of a time delay to significantly add this room induced ambience. However, it makes sense that these reflections will be heard loud and clear as PART of the music. Ideally, you would want a speaker that has an off-axis response that when the sound is reflected/absorbed still sounds like the on-axis but there is no certain way to do this in every car. So, the most logical and common sense solution would seem to be making sure your off-axis and on-axis response character matches up. From what I've seen, many of the most expensive car speakers seem to follow this logic. The Focal Utopia Be 3-way comps have fantastic off-axis response plots and they are arguably one of the best sounding car comps you can buy. I'm not convinced it's due to any fantastical or revolutionary material or motor design. My bet is that if I can design a similar high quality speaker system with the same great off-axis response I'll get very similar results.

But of course I could be tspencing on this whole hypothesis. I fully intend to put my money where my mouth is. When the drivers I want are available, I will buy them and hold them for later projects. There are two very cool projects I'd like to do and it makes me wish I had two cars. One is to adapt the best home speakers I've heard to a car setup by buying the exact raw drivers and tuning an active setup to voice them similarly. The other project is to develop a speaker system around getting excellent off-axis response.


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## rlee777 (Apr 28, 2009)

Andy Wehmeyer said:


> In a car it's sufficient to design a speaker system that won't have any obvious holes or peaks in the response due to drastically different speaker directivity at crossover points and then to equalize the response at the listening position (essentially the power response) so that it has some substantial bass boost, which is necessary in small rooms, and a high frequency response that falls gradually from about 1k up to 20k. With the exception of the bass boost, this curve looks like the power response of a speaker designed to sound good in rooms.


Thanks for this Andy. I often wondered why the small confines of a car necessitated a different EQ target (Bass Boost, tapered highs) than my home theater to sound "right". I thought it was related to road noise, but the key parameter is the size of the cabin. This was enlightening...


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## Fast1one (Apr 6, 2007)

Lets put it this way. If the speaker system in question has an off-axis response that drops off like a rock compared to on-axis, you are going to experience a very narrow sweet spot.

In a car this may not be very important as the early reflections contribute greatly to the overall sound. In addition, most people build the systems for one person: the driver. However, I also prefer to not have my head in a vice. 

Building a two seater car absolutely requires the off axis response response to mirror on axis. Otherwise, you can't fix the tonality for both listeners. This can be done to some extent by keeping the crossover point of the midrange below the beaming point of the speaker. In addition, using a small diameter tweeter doesn't hurt, but we are not as sensitive up there anyway,


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## tspence73 (Oct 14, 2008)

Fast1one said:


> Lets put it this way. If the speaker system in question has an off-axis response that drops off like a rock compared to on-axis, you are going to experience a very narrow sweet spot.


Yep.



> In a car this may not be very important as the early reflections contribute greatly to the overall sound. In addition, most people build the systems for one person: the driver. However, I also prefer to not have my head in a vice.


Ditto



> Building a two seater car absolutely requires the off axis response response to mirror on axis. Otherwise, you can't fix the tonality for both listeners. This can be done to some extent by keeping the crossover point of the midrange below the beaming point of the speaker. In addition, using a small diameter tweeter doesn't hurt, but we are not as sensitive up there anyway,


I believe it should be very possible for a sound processor to fix tonality for multiple seated positions if the off-axis response mirrors the on-axis response. That's the crux behind my design idea.


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## VP Electricity (Apr 11, 2009)

tspence73 said:


> If anything, my common sense tells me...


I think the first two words are the key...


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## Mosho (Apr 17, 2009)

Are you guys sure about most of what we hear being reflected sound? I thought that wave lengths above 1500hz were pretty short, though I don't have any real knowledge on the subject.


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## VP Electricity (Apr 11, 2009)

dbiegel said:


> I've noticed lately that there's a new "forum boner" myth of sorts emerging: that off-axis response should mirror on-axis response...
> So anyway, I'm not meaning to be a jerk or anything, but I guess I just don't get where this off axis should mirror on axis concept came from. Intuitively, it doesn't make sense to me and in fact goes against much of what I've researched, experienced, and experimented with in a car (though it makes some sense to me for a home or studio). Am I the only one who feels this way?


The basics are like this:

From a physics perspective, every piston driver will have an off-axis response which varies from its on-axis response above a certain frequency, which is dictated by the diameter of the piston. This is not necessarily the performance of the _speaker _- if we use the term driver to describe the individual driver, but the term speaker to describe the entire speaker system, including crossover points and installation modes. 

The vast majority of car speakers (not of car speakers those in this forum install, but of car speakers as a category) are installed off axis. 

For this reason, on-axis response is not neccesarily the right way to predict the response of speakers installed off-axis. 

So many speaker companies assume an off-axis install, and attempt to design a component system which has non-linear on-axis response in order to have closer to linear off-axis response. 

This kink doesn't affect DIYMA members as much, since they will often install a speaker in complicated and potentially - shall we say, non-OEM-appearing ways, to get the response they want, on or off axis. But for those of us who strive for the greatest possible fidelity in OE locations and in stock-appearing vehicles, this becomes important. 

It is one of the many reasons that DIYMA members often choose drivers not intended for car use - car-intended drivers often have compromises.

But back to your question. Ideally, a driver's response on and off axis is consistent so that the sweet spot is larger. Since physics precludes this with dynamic drivers above some frequency, some use other driver types to come closer to attaining this. it has always been a theoretical goal which has been practically unattainable, so I've never worried about it too much.


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## Oliver (Jun 25, 2007)

Some use devices to deflect sound away from the expected on axis response and beaming tendencies, also.

They look like a projection in the middle of the speaker , sometimes


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## 14642 (May 19, 2008)

The word "mirrors" is a bad one to use in this discussion. IF the off axis response is the same as the on axis response, and the on axis response is flat, the speaker will sound too bright. The on axis response should be flat and the off axis response should taper downward with increasing frequency. 

It isn't possible using current loudspeakers in existence without proprietary DSP filtering to build a speaker that has the same on-axis response as off axis response anyway. Fortunately, that isn't necessary. 

This thread has digressed into the realm of myth. If you want the facts. Read a book. I've posted the title of a good one that's written so most of you can understand it and it's available on Amazon. 

Or, continue to read and post a bunch of IMO or even IMHO posts that simply steer people in the wrong direction based on a bunch of guesses and half-baked "proofs". 

The world isn't flat, even though you may not have ever noticed the curve of the horizon.


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## capnxtreme (Feb 5, 2008)

Shut the hell up, Tspence.


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## dbiegel (Oct 15, 2006)

My experience has been pretty much the opposite of most of what has been posted here. It really seems to be true that most of what we hear in a car is glass. 

Certainly, dispersion is important... but the key, IMO, is _controlled_ dispersion. Simply using drivers with phenomenal off axis response, because you're using them off axis, is a recipe for disaster. If you've ever played with, say, dome midranges on the dash (or even in the kicks), you know what I mean. The reflections cause all sorts of phase/time issues, make the sound harsh, peaky, and bright, smear imaging, etc. Hell, most of the people I know who are serious into competing hate speakers with great off axis response, and tend to be moving toward those with poor off axis (like ring radiators).

Obviously, this is totally different from the home environment. In a home, who wants speakers that sound like garbage everywhere in the room except at a defined listening position? In a home, the walls are far away, there's a lot of absorption, and the delayed attenuated reflections can really add a lot of ambience....

In a car, we sit in one exact spot, all the time. That's a HUGE asset and probably the biggest advantage we have compared to the compromises a home system has to make. Now imagine you're a Harman engineer, and you have to design a system for a tiny glass cube with two recliners and some asymmetrical reflective surfaces randomly placed inside. Would you still want a great off axis response? Think about it... that's pretty much what the car environment is.


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## dbiegel (Oct 15, 2006)

Andy Wehmeyer said:


> IF the off axis response is the same as the on axis response, and the on axis response is flat, the speaker will sound too bright. The on axis response should be flat and the off axis response should taper downward with increasing frequency.


That's been my experience too... and it happens to describe the typical speaker with poor or average off axis response as well... beaming seems to be a good, very good thing in a car...



Andy Wehmeyer said:


> This thread has digressed into the realm of myth. If you want the facts. Read a book. I've posted the title of a good one that's written so most of you can understand it and it's available on Amazon.
> 
> Or, continue to read and post a bunch of IMO or even IMHO posts that simply steer people in the wrong direction based on a bunch of guesses and half-baked "proofs".


Andy, the reason I started this thread in the first place was to debunk this myth and keep it from steering newcomers in the wrong direction (or to find out that I am wrong, and learn something!). Now, I'm sure most of us come to a forum like this to meet other people interested in the same hobby, learn something, discuss ideas, etc. and IMO it's not cool that you're telling people to F off and go read a book. I certainly didn't expect that from you -- bad day? I haven't read that book, but I doubt it has much discussion of the car environment. Of course, the general rules of acoustics and physics don't change, but the way you _apply_ them to a car environment tends to be tricky and very different from other environments.


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## tspence73 (Oct 14, 2008)

> It isn't possible using current loudspeakers in existence without proprietary DSP filtering to build a speaker that has the same on-axis response as off axis response anyway.


Acutally, you can't get the precise response but you can get really, really close. Look at the response graphs from the Focal Utopia Be 3-way. It's virtually identical on and off axis in frequency response except the off-axis is just like 3-4db lower in volume. The x-overs are setup to rolloff the driver before it's off-axis rolloff starts up. That is what I observe and it's my hypothesis that if you setup a speaker system's off-axis response to always be optimum along it's intended range, you'll get way better reponse at multiple seated positions. If I'm wrong, I'll find out because I'm going to test it out myself. I've viewed off-axis response plots on woofers, mids and tweets and it's very possible to do this.


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## cvjoint (Mar 10, 2006)

tspence73 said:


> I believe it should be very possible for a sound processor to fix tonality for multiple seated positions if the off-axis response mirrors the on-axis response. That's the crux behind my design idea.


:thinking2: :lol:

If you think about it the car is nice from one point of view, the driver will always sit in the same spot and will have minor changes of head position. Given that you use conventional dome, woofer speakers outside of the beaming domain or close to on axis u won't need perfectly equal response on and off axis. Regardless, this is unachievable like Andy mentioned, I've seen enough car waveguides to know it's wishful thinking. Even with the perfect speakers you are not sitting in an empty room, as your head moves you are in a different position with regards to the car panels, different reflections etc

Don't even get me started on two seater systems, the only way that's going to happen is in a McLaren F1 if you hold a baby in the driver's seat.


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## [email protected] (Jun 12, 2008)

capnxtreme said:


> Shut the hell up, Tspence.


x 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000


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## michaelsil1 (May 24, 2007)

tspence73 said:


> Acutally, you can't get the precise response but you can get really, really close. Look at the response graphs from the Focal Utopia Be 3-way. It's virtually identical on and off axis in frequency response except the off-axis is just like 3-4db lower in volume. The x-overs are setup to rolloff the driver before it's off-axis rolloff starts up. That is what I observe and it's my hypothesis that if you setup a speaker system's off-axis response to always be optimum along it's intended range, you'll get way better reponse at multiple seated positions. If I'm wrong, I'll find out because I'm going to test it out myself. I've viewed off-axis response plots on woofers, mids and tweets and it's very possible to do this.


The Be's sound very different on axis vs. off axis.



My new Car System:


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## tspence73 (Oct 14, 2008)

BeatsDownLow said:


> x 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000


You know. I don't want to hear from the idiots who have no idea what I'm talking about nor have they done ANY research on the subject yet think just because someone knowledgable chimes in that somehow that gives them some kind of green light to start giving me crap. 

Again, do some research before you start jumping out into the street like a mob with pitchforks to lynch tspence.

Check out these off-axis response plots from one of the most expensive and respected car speakers on the market then come back and talk **** if you have any good insight:

Response plots of Utopia Be kit no 7

6 W3 Be

3 W2 Be

TBe

Notice the excellent off-axis response across it's intended range of use. Only the tweeter falls off at around 10KHz which isn't a big deal. Everything else appears set to give incredible off-axis response when the crossover is applied. 

Now, if you have any comments, by all means, please tell me how my idea is "bad" when one of the best speaker systems in the world has the very ideal plot I'm wanting to try. And don't give me anymore BS about how these don't sound very similar on and off axis. That response graph clearly shows it's got a little variation but it's DAMN close.


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## michaelsil1 (May 24, 2007)

tspence73 said:


> Check out these off-axis response plots from one of the most expensive and respected car speakers on the market then come back and talk **** if you have any good insight:
> 
> Response plots of Utopia Be kit no 7
> 
> ...


Have you heard them?


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## [email protected] (Jun 12, 2008)

michaelsil1 said:


> Have you heard them?


No but its Spence, he has to right, and spence no one gives a **** what you "think"


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## michaelsil1 (May 24, 2007)

michaelsil1 said:


> Have you heard them?





BeatsDownLow said:


> No but its Spence, he has to be right, and spence no one gives a **** what you "think"


I was hoping for a yes  then he would know that the Be's sound very different On Axis vs. Off Axis regardless of what the graphs say.


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## tspence73 (Oct 14, 2008)

Those response plots do not lie. Anyone reading this thread can access the same data I did. Look for yourselves and decide if I'm full of it or if I have a legit point here. I believe I do.


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## tspence73 (Oct 14, 2008)

michaelsil1 said:


> I was hoping for a yes  then he would know that the Be's sound very different On Axis vs. Off Axis regardless of what the graphs say.


That would depend on how the crossover is set but most of the places you would choose for a HP/LP point look pretty darn good to me on/off axis. Unless the woofer LP is set above 1.5KHz where it jumps up or the mid is LP above 3.5KHz with a wide octave slope then you would have a good deviation.


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## michaelsil1 (May 24, 2007)




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## capnxtreme (Feb 5, 2008)

tspence73 said:


> You know. I don't want to hear from the idiots who have no idea what I'm talking about


Dude, YOU have no idea what you're talking about.

Sorry to break it to you, but low-passing drivers before they beam is not a revolutionary idea.


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## tspence73 (Oct 14, 2008)

capnxtreme said:


> Dude, YOU have no idea what you're talking about.
> 
> Sorry to break it to you, but low-passing drivers before they beam is not a revolutionary idea.


Revolutionary or not. I had you trying to clown on me for no good reason. So, just lay off and only post if you have something to say that adds to the conversation.

BACK to what this thread is about. It is rather obvious to me that maintaining good off-axis response throughout the usable range of the drivers CAN produce excellent sound as evidenced by what I've linked up. It's by no means a guarantee that your sound will be awesome but with a nice processor I see no reason why it shouldn't sound like a world class setup.


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## capnxtreme (Feb 5, 2008)

Actually, there's a very good reason, and we've told it to you before: When you misrepresent yourself as knowledgeable on a subject, it decreases the value of the forum, and it confuses newbs. A little humility would go far.


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## InterHat (May 12, 2008)

tspence73 said:


> Revolutionary or not. I had you trying to clown on me for no good reason. So, just lay off and only post if you have something to say that adds to the conversation.
> 
> BACK to what this thread is about. It is rather obvious to me that maintaining good off-axis response throughout the usable range of the drivers CAN produce excellent sound as evidenced by what I've linked up. It's by no means a guarantee that your sound will be awesome but with a nice processor I see no reason why it shouldn't sound like a world class setup.


It's not going to matter. Take a flashlight and shine it in your car in the dark. Then shine it indoors. Light scatters completely differently and gives a different color, brightness, feel depending on the surrounding materials due to diffraction, absorption etc. Sound is going to behave somewhat similarly. The hard plastics will reflect certain frequencies and soft fabrics will absorb others. The minimal gain from your efforts to make good off axis response in a car will be defeated by surface reflections and absorption of certain frequencies. 

You may see a SLIGHT benefit but only if you're doing some pretty intense tuning with an RTA and you're still going to need to time align if you have different path lengths.

Working in a car is not like working in a room. You don't have an equilateral triangle, you have very little control over your reflection surfaces, and there's a ton of outside noise. Treating it like you're working in a listening room is just going to waste your time and money. You really need to start listening to people here more or you're going to end up in another 6x9 subwoofer fiasco.


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## 03blueSI (Feb 5, 2006)

Tspence, if you just go off of graphs for everything you will have no understanding of a car environment. If we believed anechoic graphs and used it to represent in car response we would have no response from subs below 20-40 hz. We know this is not the case.

You have to consider the environment. A speaker reacts differently anechoically (the way speakers are typically measured) than they do in a large hall, average size living room, small room, extremely small studio, or in a car.


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## tspence73 (Oct 14, 2008)

03blueSI said:


> Tspence, if you just go off of graphs for everything you will have no understanding of a car environment. If we believed anechoic graphs and used it to represent in car response we would have no response from subs below 20-40 hz. We know this is not the case.
> 
> You have to consider the environment. A speaker reacts differently anechoically (the way speakers are typically measured) than they do in a large hall, average size living room, small room, extremely small studio, or in a car.


Let me ask you a question. If I buy drivers that show a graph that comes very close to these world class ones, then would you not expect them to deliver very similar sonic results when all other things are equal? That's my point. Find a really good model and follow it. I think I can take this model and maybe even _improve_ on it. The XBL Tang Band ceradome tweeter crosses VERY low and it's off-axis roll-off doesn't start until 15KHz. That is intriguing to me. Until this tweeter came along I didn't think I could pull off the idea without a ton of graph reviews and driver comparisons. Now I think I can do it with rather mainstream drivers. I wouldn't mind finding an XBL 4" mid that can do 300Hz with really good SPL output.


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## 14642 (May 19, 2008)

dbiegel said:


> That's been my experience too... and it happens to describe the typical speaker with poor or average off axis response as well... beaming seems to be a good, very good thing in a car...
> 
> 
> 
> Now, I'm sure most of us come to a forum like this to meet other people interested in the same hobby, learn something, discuss ideas, etc. and IMO it's not cool that you're telling people to F off and go read a book. I certainly didn't expect that from you -- bad day? I haven't read that book, but I doubt it has much discussion of the car environment. Of course, the general rules of acoustics and physics don't change, but the way you _apply_ them to a car environment tends to be tricky and very different from other environments.


My point is that I posted a link to a very simple powerpoint presentation prepared by one of the world's premier acousticians that explains the concept of directivity, which is what we're talking about here. I also posted the title of a book that includes a very detailed explanation written by the same acoustician. I also posted a brief synopsis of the information in my own words as it pertains to cars. VP Electricity also posted the same information in somewhat more detailed form. 

There are some basic truths here that have been proven and have been long accepted as good science. Since I have access to plenty of documents and plenty of the scientists who do this work, I thought I'd provide access to some of it here. My insistence that good research performed by qualified scientists is similar to truth isn't telling people to F-off. 

If you use a system of speakers that is designed, along with it's crossover (passive or active) to provide flat response when measured on-axis, but you don't take into account the off axis response, you're asking for trouble. The dispersion of drivers narrows as the frequency rises and that's a function of the driver diameter (or radius). If you use a big midrange and a small tweeter and a crossover point that's within the range where the midrange's dispersion is narrow, you may have a flat on-axis response, but there will be a hole in the off axis response. The tweeter's dispersion will be wide at that frequency, so the off axis response of the tweeter will be louder in that region. That's what makes the hole a hole and not a gradual rolling-off at high frequencies. There's a picture of this in the book and also a graph in the powerpoint. 

Now, put that system in a car and you'll hear the on-axis response if the speakers are mounted on-axis. The off axis response will be reflected and will eventually make it to your ears, combined with the on-axis response. You'll hear the hole. 

Now, if you mount the speakers off axis, you'll hear the off axis response as the primary sound and the on-axis sound will be reflected off of all the surfaces and will eventually make it to your ears. It will be combined with the direct off-axis response and you'll still hear the hole.

The difference between cars and rooms is that the reflective surfaces are much closer--and, as you've pointed out--are probably more reflective at VERY high frequencies than a room because the glass is smoother than the sheetrock (not that much smoother, though). Since the reflective surfaces are much closer in cars than in rooms, the magnitude (loudness) of the reflections is greater--the inverse square rule describes this condition--sound intensity is reduced by 6dB for every doubling of distance. 

Because the reflective surfaces are much closer and the reflections are louder, the off axis response is more important in the car than in a room. Wait, maybe I should repeat that...

Because the reflective surfaces are much closer and the reflections are louder, the off axis response is more important in the car than in a room. 

The reflective surfaces in the car are irregular, unlike the walls in the room. Cavities have resonance and those resonances contribute the the reflected sound, just like the simple reflections from the rest of the surfaces. These modify the reflected sound. 

One could aask, "Wow, with all of those reflections, how could you even begin to predict what the car will actually sound like?" That would be a good question. Fortunately, because all of the reflections arrive at your ears at nearly the same time as the initial sound, we can eliminate one source of the problem by ensuring that there are no BIG PEAKS OR HOLES in the off axis response and that the off axis response of the speakers tapers down smoothly, so the system doesn't sound too bright. (If this is what TSpence means when he writes "mirrors" then we're on the same page and he gets it). Then, we can EQ the whole thing, direct and reflected sound according to a desired target response at the listening position. The irregularities in the reflected sound will still exist. 

If you want to change the shapes of the interior panels to eliminate some of them, that's some additional work that may be beneficial, but if you do it by conjecture and trial and error, it's very expensive and time consuming and you may end up with something that can't be driven. Plenty of IASCA competitors love to talk about how they remove the steering wheel to eliminate a reflection, but I've never talked to on who could tell me at what frequency the reflection caused a problem and why--they tell the judge this and the judge scratches his head and gives away a point.

It's important to remember that for measurement's sake, on-axis usually means "directly in front of the speaker". When you mount the speakers in your car, you can choose to mount them in a way that the measured on-axis response is directed at you or directed away from you. In either case, wht you hear in the car is the sum of all of the sound radiated from the speaker and reflected toward your ears. The reflected sound is a big contributor. With a speaker designed as I've described above (flat on axis and a gentle downward taper at higher frequencies), aiming the speaker away from the listening position removes high frequency from the response you hear. If it isn't designed as I've described above, but has a reasonably flat on-axis response and big holes and peaks in the off axis response, then mounting it so it doesn't point at you adds the irregular response to the sound you hear and attenuates the flat response from the sound you hear. Is this better? Maybe, if you're lucky enough to have a speaker system with holes where your car provides peaks and peaks where your car provides holes. 

It isn't credible to suggest that for all applications and all cars, it's best to point them away, because in many applications those peaks and holes don't cancel each other. Suggesting that will steer more people away from success than toward it. 

Designing a speaker system with it's crossover to provide the correct response in a particular car is a much more precise exercise than what is being espoused here when people posit that choosing a speaker with "bad off axis response" is better because IASCA winners do it or because "I heard a car that had those "SilkyPristineAudio" speakers in it and the curve in the brochure looks good, so the entire system design and whatever EQ is in the car doesn't matter because I like to simplify. Curve in brochure = good. Car sound = good. Brochure = truth = science = plausible and complete explanation." 

I have speakers mounted so that they fire into the glass and yes, the reflection causes a hole in the sum of the direct sound and the reflection. Is it a problem? Well...I was able to fix the frequency response well enough with an EQ. The benefit of the location is that the vocals and center information is precisely located where it should be.


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## tspence73 (Oct 14, 2008)

Andy,

On a slightly different acoustic topic. Do you think it's possible to hand mold/create panels to replace the plastic in cars to be less reflective and more absorbent? I've been really curious if it's possible to even replace paneling with a more "acoustic friendly" surface.


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## rockinridgeline (Feb 2, 2009)

Thanks to Andy for the link to the.pdf file. Excellent reading. I now understand how the use of RTA can and different measuring positions in the car can determine if a sonic issue is caused by resonance or reflection and better plan how to correct it. It also explains why certain issues never seem to go away no matter how much eq is applied. Good stuff! We need more real knowledge like this to overcome the car environment.


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## Brian Steele (Jun 1, 2007)

Andy Wehmeyer said:


> It isn't possible using current loudspeakers in existence without proprietary DSP filtering (snip)


...or perhaps Acoustic Lens Technology  - see the B&O Beolab 5: 
http://www.bang-olufsen.com/beolab5

I've seen measurements of that beastie (or was it its predecessor? - I can't remember) - very little change in response within a 180 degree horizontal window.


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## Oliver (Jun 25, 2007)

Epic thread potential


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## donkeypunch22 (Nov 5, 2008)

Thanks Andy!


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## donkeypunch22 (Nov 5, 2008)

Oh, and for those who liked Andy's suggested article by Toole and want more, here is part 1 and part 3:

http://www.harman.com/wp/pdf/LoudspeakersandRoomsPt1.pdf

http://www.harman.com/wp/pdf/LoudspeakersandRoomsPt3.pdf


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## tspence73 (Oct 14, 2008)

Brian Steele said:


> ...or perhaps Acoustic Lens Technology  - see the B&O Beolab 5:
> http://www.bang-olufsen.com/beolab5
> 
> I've seen measurements of that beastie (or was it its predecessor? - I can't remember) - very little change in response within a 180 degree horizontal window.


Woah. You've got to be f'n kidding me. 
http://www.bang-olufsen.com/aston-martin/beosound-dbs

















:bowdown:


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## boltupright (Feb 14, 2007)

Is it possible to control/reduce the off axis sound by putting a soft material around the outer edge of a speaker and have it extend out from the speaker an inch or two? (tweeter and midrange)


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## I800C0LLECT (Jan 26, 2009)

TSpence...

After reading over the analysis between you and Andy it seems that you're on a trip or attempt to gain respect through the use of "what if?!". That's not academic.

I'd have to believe that the car environment is so scattered, attempting to try and reproduce a proper listening environment is too much of a task to tackle. That's why active tuning takes the cake in these forums. It's much easier(wish it was that easy for me) to tune a system than rip your car apart on a daily basis followed up with empirical data and RTA's to prove to the world that you have a "perfect" sound.

At that point everybody should buy a car, rip out the interior and pillars...then replace it with a big ass box allowing perfect symetry, etc. Funny images come to mind. Anyways, good reading so far guys. Bottom line seems to be go with what makes your ears happy...unless you're involved in competition. phew.

Thanks for chiming in Andy. You're good ppl.


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## dbiegel (Oct 15, 2006)

boltupright said:


> Is it possible to control/reduce the off axis sound by putting a soft material around the outer edge of a speaker and have it extend out from the speaker an inch or two? (tweeter and midrange)


Funny you mention it, that's exactly what I've been experimenting with lately... making foam "waveguides" and using them on a very wide dispersion dome midrange (Dayton RS52) to control the directivity to what I want. I'm also using the seats as a sort of quasi-waveguide as well to attenuate the angles I don't want. Props to Honda for making the LX seats basically massive blocks of foam and cloth 

I started the experiment based on a simple acoustic principle not related to this thread discussion... the fact that interaural level differences dominate the way our brains localize sounds at higher frequencies (> ~1600hz). So my hypothesis was that if you can use a waveguide of some sort to attenuate the left speaker's output to your right ear, your brain would localize the sound farther to the left. 

I've only demo'd this to a couple people but they will tell you that it was pretty much a successful experiment and pretty neat outcome... staging out past the side mirrors, almost to the B pillars...

Of course, the problem I'm having is that my door mounted midbasses totally collapse the stage  Still, it's a lot of fun to play with and it seems to be working well so far.


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## I800C0LLECT (Jan 26, 2009)

boltupright said:


> Is it possible to control/reduce the off axis sound by putting a soft material around the outer edge of a speaker and have it extend out from the speaker an inch or two? (tweeter and midrange)


From what I've read so far...changing positions of speakers would make more sense. No reason to add another variable to the installation. But this is why choosing speakers for response can be that much more critical.

Car Audio is subject to the conditions of the listener and their ears. Therefore, trial and error seems to play a bigger role than most believe(bb customers). Try different types of speakers and methods based on where you prefer to install. Then choose one that sounds best.

Attempting to find and coordinate the responses inside your car will only take you so far before an installation reveals the truth.


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## I800C0LLECT (Jan 26, 2009)

Good grief dbiegel 


Sounds pretty neat, wish I could demo that work. Apparently it takes a pretty good mind to apply the ideas 

I'm not the brightest bulb. Still soaking the sponge.


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## dbiegel (Oct 15, 2006)

I800C0LLECT said:


> Car Audio is subject to the conditions of the listener and their ears. Therefore, trial and error seems to play a bigger role than most believe(bb customers). Try different types of speakers and methods based on where you prefer to install. Then choose one that sounds best.
> 
> Attempting to find and coordinate the responses inside your car will only take you so far before an installation reveals the truth.


I couldn't agree more... regardless of how much we like to discuss acoustics, at the end of the day, trial and error is IMO the most important factor, by far. I've learned this the hard way myself with my most recent vehicle. I've never had such a hard time getting a car to sound right as this one. The mistake I made was focusing on tuning. I could get it to sound "ok" but never great... 

So I decided to go back to the drawing board and just hook up speaker wires to a couple drivers and move them around the car to see what it sounded like. It's amazing how without any tuning, there are spots that sound way better than I could ever get my factory locations or horns to sound, no matter how much processing I had used...

The funny thing is, the typical spots (kickpanels, dash pods) actually sounded the worst in my car... horrible to say the least. It's unfortunate that so many people choose their spots arbitrarily or because other people use them and then spend months or years trying to tune it to sound good, when they could perhaps have it sound even better without any tuning just by finding a good location in their car first.


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## michaelsil1 (May 24, 2007)

Danny,

Have you changed your Drivers again?


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## dbiegel (Oct 15, 2006)

michaelsil1 said:


> Danny,
> 
> Have you changed your Drivers again?


Michael, Yup yet again I did... I think those JBL Pro Audio engineers would have a heart attack if I told them I switched from their latest design to a set of cheapo fullranges I paid $20 a piece for


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## michaelsil1 (May 24, 2007)

dbiegel said:


> Michael, Yup yet again I did... I think those JBL Pro Audio engineers would have a heart attack if I told them I switched from their latest design to a set of cheapo fullranges I paid $20 a piece for


Where did you install the full ranges and are you driving up to Riverside tomorrow?


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## Fast1one (Apr 6, 2007)

Great thread. Once again, Andy, you have delivered with your well constructed responses. I don't think I have anything else to add, although the mention of waveguides got me thinking of a thread I was following a couple months back:

diyAudio Forums - Adventures in cardioid - Page 1

Cliffs: A different type of speaker alignment in an attempt to simulate a "cardioid" polar response using a "muffler" enclosure if you will. Essentially a stubby cylinder with the driver mounted to one of the sides and the curved part stuffed like an aperiodic enclosure. Requires a lot of experimentation and measurement though. I was going to attempt it but im getting tired of doing so many experiments with car audio ( even though it often times is very revealing to the limitations of traditional woofer and tweeter systems). I am just going to go ahead and go full range again. That was by far my favorite. 

Some one should try it! Here is a link that got me thinking as well, which is mentioned in that thread. This company perfected the use of these muffler/radiator alignments:

http://www.gradient.fi/file_download/15/Basis_of_stereo_Gradient_design.pdf

That link is a gem in many regards. For example, In it you will find a VERY intriguing multiple array tweeter concept that some of you DIYers may want to try. 


> Treble sound reproduction was dealt with a line source, which consisted of four drive-units.
> The effective length of the line source was shortened electronically. The lowest treble
> frequencies were reproduced by all four units, the highest by only one. Thus the directivity
> was controlled in desired manner.


Lots of great general info about audio as well. Short read, and pretty informative. Though a bit conservative since they didn't want to give out too many company techniques. 

Read, absorb, test!

Regards,

Serg


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## Oliver (Jun 25, 2007)

dbiegel said:


> I couldn't agree more... regardless of how much we like to discuss acoustics, at the end of the day, trial and error is IMO the most important factor, by far. I've learned this the hard way myself with my most recent vehicle. I've never had such a hard time getting a car to sound right as this one. The mistake I made was focusing on tuning. I could get it to sound "ok" but never great...
> 
> So I decided to go back to the drawing board and just hook up speaker wires to a couple drivers and move them around the car to see what it sounded like. It's amazing how without any tuning, there are spots that sound way better than I could ever get my factory locations or horns to sound, no matter how much processing I had used...
> 
> The funny thing is, the typical spots (kickpanels, dash pods) actually sounded the worst in my car... horrible to say the least. It's unfortunate that so many people choose their spots arbitrarily or because other people use them and then spend months or years trying to tune it to sound good, when they could perhaps* have it sound even better without any tuning just by finding a good location in their car firs*t.


I have noticed people limit themselves  [the bad set-ups are the easiest though on a positive note  ].


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## boltupright (Feb 14, 2007)

dbiegel said:


> I couldn't agree more... regardless of how much we like to discuss acoustics, at the end of the day, trial and error is IMO the most important factor, by far. I've learned this the hard way myself with my most recent vehicle. I've never had such a hard time getting a car to sound right as this one. The mistake I made was focusing on tuning. I could get it to sound "ok" but never great...
> 
> So I decided to go back to the drawing board and just hook up speaker wires to a couple drivers and move them around the car to see what it sounded like. It's amazing how without any tuning, there are spots that sound way better than I could ever get my factory locations or horns to sound, no matter how much processing I had used...
> 
> The funny thing is, the typical spots (kickpanels, dash pods) actually sounded the worst in my car... horrible to say the least. It's unfortunate that so many people choose their spots arbitrarily or because other people use them and then spend months or years trying to tune it to sound good, when they could perhaps have it sound even better without any tuning just by finding a good location in their car first.



You're right of course but just wondering if anyone has tried it or if they thought it might work for limiting off axis response. I am moving my speakers around, and plan to try it out. Also thinking of putting my tweeters and midrange on a swivel to help dial in the sound.


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## dbiegel (Oct 15, 2006)

michaelsil1 said:


> Where did you install the full ranges and are you driving up to Riverside tomorrow?


You wouldn't believe me Michael if I told you where I installed them  It's a place I've never heard of anyone putting speakers before. I have them aimed precisely so that they reflect off the glass to your ears... and I just use foam "waveguides" to modify the directivity as needed..

It's weird, but somehow, man, it just works. The only problem is that the passenger side has the worst sound I've EVER heard in a car... I mean, the best way I can describe it is it sounds like an old, half-blown alarm clock radio has been installed in the glove box...LOL


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## cvjoint (Mar 10, 2006)

You crazy kid! I want to see this tomorrow too.

The problem with finding the right spot is that it does take 1 year to find out if it's good or not. I imagine most people's way of 'trying out' a spot is to throw a towel and blast it for 30 minutes, I don't think that's of any use. You want to to pick the spot, try to build an ideal enclosure for the speaker, a sturdy baffle, then spend a few months tuning and listening to really get a feel for it. There may be many challenges that you won't see in the one day you gave it a try, the sun might distroy the speaker in short time, passengers block sound considerably, maybe you can't even find enough airspace to build the enclosure anyway.


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## 14642 (May 19, 2008)

tspence73 said:


> Andy,
> 
> On a slightly different acoustic topic. Do you think it's possible to hand mold/create panels to replace the plastic in cars to be less reflective and more absorbent? I've been really curious if it's possible to even replace paneling with a more "acoustic friendly" surface.


I've heard a couple of cars in which the installer believed he had done this--in fact, he must have because the car sounded lifeless to me--sounded like a huge pair of 15" headphones. Those cars did other things well, but those areas of performance were unrelated to this. I think it's a waste of time and I don't really like the sound of "dead" rooms, especially with 2-channel set-ups. Multi-channel setups make this less necessary, since the sides and rears can be used to add the reflections of a different space. 

This is also explained in great detail in Floyd's book. I really suggest that those of you who are serously interested in this stuff buy it and use it as a reference. It'll save you lots of time, lots of money and you'll have a thousand head-slapping--"no ****...that's why that happens" moments while you read it.

I wish I had been a serious competitor in the 90s so I could have plunked down some cash for "teardowns" of some of the most famous cars. You wouldn't believe the ********. Some of it is the cause of all this consternation over speaker placement, reflections, optical signal connections, etc.


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## Fast1one (Apr 6, 2007)

cvjoint said:


> You crazy kid! I want to see this tomorrow too.
> 
> The problem with finding the right spot is that it does take 1 year to find out if it's good or not. I imagine most people's way of 'trying out' a spot is to throw a towel and blast it for 30 minutes, I don't think that's of any use. You want to to pick the spot, try to build an ideal enclosure for the speaker, a sturdy baffle, then spend a few months tuning and listening to really get a feel for it. There may be many challenges that you won't see in the one day you gave it a try, the sun might distroy the speaker in short time, passengers block sound considerably, maybe you can't even find enough airspace to build the enclosure anyway.


All good points, but I think there are times when its plainly obvious that the speakers sound better in a particular spot. This all depends on the car in question of course. 

Personally, I have given every position in my car a chance, including kick panels. I could never get it to sound nearly as good as an A-pillar install, for my particular car. As a result, I keep going right back to A-pillars, and I expect my next install to not change any time soon.


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## dbiegel (Oct 15, 2006)

Well for those of you asking about the domes under the chairs reflected off the windshield experiment, it turned out to be a total failure  The only thing that was really cool about it was that the stage width was unbelievable... past the side mirrors... but as soon as my door mounted midbass are added into the equation and after a bunch of foam to attenuate the off axis to the underdash, the width collapses to the pillars... time alignment also seems to have collapsed it for some reason.

and so I'm left with stage too much in your face, imaging is diffuse. Height is really weird. I've had some people tell me that its at the roof level, others that its down around center dash or even lower at the sides... same thing with the center. Some find it solid center windshield, others can't even locate it at all. The funny part is, it sounds totally different to me at different times, too. I don't know what to make of it... it might depend on your exact position and how you hold your head, or individual HRTFs, or maybe I somehow fooled myself into sometimes thinking it was centered and high. Funny how these things work... if I focus on the center of the windshield looking for the center, and turn my head the right way, the sound is right there... must be a psychological thing.

It also has a "layered" soundstage of sorts... lower frequencies tend to sound vertically lower than higher frequencies. I think this is a combination of two things... First, my foam isn't nearly thick enough to do anything at lower frequencies, so they still bounce off the underdash.. only the much higher frequencies have the directivity controlled... hell, maybe low frequencies are even diffracting somehow around the chair and around my body to go straight up from below. Second, my midbasses also bring the sound way down, since I have to play them high enough to mate with the domes, which, unlike cone midranges, can only cross down at 500 or so.

Anyway, it was certainly fun to play around with. Maybe I just somehow screwed up the time alignment or phasing, but I think I'm simply gonna go back to the drawing board. If anyone else experiments with something like this please post here as I'd love to hear about other experiences with a reflection based setup.


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## michaelsil1 (May 24, 2007)

The thing about crazy ideas is sometimes they work, keep it up.


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## Fast1one (Apr 6, 2007)

michaelsil1 said:


> The thing about crazy ideas is sometimes they work, keep it up.


Agreed, people thought I was crazy when I told them about my experiments with full range drivers about a year ago. Now look at the recent influx of believers. 

Just goes to show you how scared most people are to break away from the norm. Traditional 2-way has so many problems yet many still refuse to have it any other way. 

3-way is a much better option but it can get expensive very fast with the processing, amplification, and driver cost. 2-way with full range driver just makes so much more sense on a budget and reduces complexity for beginners.


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## VP Electricity (Apr 11, 2009)

Fast1one said:


> Agreed, people thought I was crazy when I told them about my experiments with full range drivers about a year ago. Now look at the recent influx of believers.


Doesn't mean you're not crazy...


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## cvjoint (Mar 10, 2006)

VP Electricity said:


> Doesn't mean you're not crazy...


:laugh:



Fast1one said:


> All good points, but I think there are times when its plainly obvious that the speakers sound better in a particular spot. This all depends on the car in question of course.
> 
> Personally, I have given every position in my car a chance, including kick panels. I could never get it to sound nearly as good as an A-pillar install, for my particular car. As a result, I keep going right back to A-pillars, and I expect my next install to not change any time soon.


What do you call a chance? After I learned to use testing software at a bare minimum I sadly realized all my previous installs are meaningless, either because I now have much better box modeling skills or I haven't tried to EQ out the imperfections with the WinMLS. The thing is some spots may plain suck but what if a proper install and tunning with software assist can make it work, vs a better out of the box spot that will never ever achieve that potential because it's cursed from the beginning with unequable nulls. 

Every few it's probably best to go back to an experiment that failed and try at the very lest to learn why it did, without doing so you are setting yourself up for more problems down the road. 

Danny I hate to sense a bit of discouragement from your last post. I think your experiment was brilliant and partially a success story. I did not know a dome that large can be so manageable on both ends or that odd location could sound great and stage great. If a bit more depth could be achieved I would have claimed a flat out winner.


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## dbiegel (Oct 15, 2006)

cvjoint said:


> Danny I hate to sense a bit of discouragement from your last post. I think your experiment was brilliant and partially a success story. I did not know a dome that large can be so manageable on both ends or that odd location could sound great and stage great. If a bit more depth could be achieved I would have claimed a flat out winner.


Thanks George, it was definitely an interesting and fun learning experience. Maybe I'll play around with the phasing and time alignment some more and see what happens before I scrap everything. The success to me is that the IASCA judge thought the mids and highs were very good tonally...got super high scores in those (just a big peak around 2khz, which I really should have tried to tune out since I saw it on the RTA before the show). That's pretty neat I think, considering everything from 500 and up was being played from a single driver essentially under a chair.


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## Fast1one (Apr 6, 2007)

VP Electricity said:


> Doesn't mean you're not crazy...


Nothingwrong with a little crazy 



cvjoint said:


> :laugh:
> 
> 
> 
> ...


Just a different way to tackle things. Im just explaining that there is more than one way to skin a cat, while you are telling me that I CAN'T skin a cat 

I have never reached the point where i couldn't equalize a null or peak. Then again, I don't use traditional door midbass installations or traditional IB alignments 

To each their own though. I only use measurement software to troubleshoot if nothing has worked for me, which is uh, never. If you use some intuition, you can generally figure out what is really going on.


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## FoxPro5 (Feb 14, 2006)

boltupright said:


> Is it possible to control/reduce the off axis sound by putting a soft material around the outer edge of a speaker and have it extend out from the speaker an inch or two? (tweeter and midrange)


It's very difficult to say if what I did with my tweeters affected the overall response without RTA measurements or blinded testing, but to me it seems that using an absorber near the most reflective edge of the speaker does have a positive effect. Dare I say it sound's "cleaner" with more "body" with the material in place then without?

Who knows, sometimes it's better not to tie your neural network in a knot on this stuff and just get in your car and listen and decide that way. Over thinking, over analyzing separates the body from the mind....[Tool]........


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## Fast1one (Apr 6, 2007)

FoxPro5 said:


> It's very difficult to say if what I did with my tweeters affected the overall response without RTA measurements or blinded testing, but to me it seems that using an absorber near the most reflective edge of the speaker does have a positive effect. Dare I say it sound's "cleaner" with more "body" with the material in place then without?
> 
> Who knows, sometimes it's better not to tie your neural network in a knot on this stuff and just get in your car and listen and decide that way. Over thinking, over analyzing separates the body from the mind....[Tool]........


Thats not surprising, I am actually about to try it on my dad's truck since I couldn't get creative with his install ( had to go two way midbass in door, UGH). The tweeter are mounted in the stock locations on the sail panels. I think adding a small amount of absorbent material on the edge of the dash will help. Maybe my dad won't notice it there


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## BigRed (Aug 12, 2007)

don't give up danny. i tried many things in my truck before settling on what I did. you'll get it.......keep experimenting bro 

pm me if you're interested in the power supply for your processor


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## Patrick Bateman (Sep 11, 2006)

dbiegel said:


> I've noticed lately that there's a new "forum boner" myth of sorts emerging: that off-axis response should mirror on-axis response. It seems to have begun in the discussion of Patrick Bateman's awesome unity waveguide project...
> 
> So anyway, I'm not meaning to be a jerk or anything, but I guess I just don't get where this off axis should mirror on axis concept came from. Intuitively, it doesn't make sense to me and in fact goes against much of what I've researched, experienced, and experimented with in a car (though it makes some sense to me for a home or studio). Am I the only one who feels this way?
> 
> Maybe I'm just confused and I will certainly try to keep an open mind. I'd love it if someone could either explain to me the theory of why this is beneficial in a car, and/or point me to some white papers etc that back this theory up.


I hate to say this, but you actually have it completely backwards. In my car I am designing the speakers so that they're MUCH quieter off-axis than on-axis.

The main reason I am doing this is to create a solid center image. I am cross-firing the speakers. Because the speaker that's closest to you is pointed the other way, and it's quieter off-axis, it pulls the image towards the center of the car.

A side benefit of this arrangement is that it reduces reflections off the side windows.

Does that make sense? There's a ton of illustrations on the first page of the thread.

Illustrations are academic though, what really counts is how it works in the real world. Let me demonstrate how well it's coming along.

Before reviewing my measurements, please understand that these aren't from an anechoic chamber. These are actual measurements from my car. There are peaks, dips, and valleys, which simply can't be avoided. It's a reflective environment.

The main idea is that they're minimized, and we're controlling the directivity.

Without further ado, let's start with a graph of five inch two way, measured on and off-axis. What you'll see is that the off-axis response looks nothing like the on-axis. There's a big suckout in the midrange, and a peak in the treble. That's the problem when you design a speaker to only sound good on one axis.










Next, let's take a look at a commercial car audio waveguide. I mounted it under my dash, and measured it on and off axis, from zero to 45 degrees. 

Remember that the OFF axis sound needs to be QUIETER than the on-axis, if the waveguides are cross-fired.

You'll notice that the shape of the curves fit in a narrow window, which is good. What's bad is that it's not quieter off-axis than it is ON axis. In fact, some frequencies are significantly LOUDER off-axis than they are ON axis. This will make the image wander all over the dash. Another problem is that one angle there are peaks and dips, and then they disappear at another angle. Ideally we want all the curves to look identical, but off-axis it should be lower in volume.

I don't mean to sound hyper-critical. These commercial waveguides are actually a big improvement over a conventional two-way, but they're not perfect.










Finally, here's a set of measurements of my Unity waveguide. The red line is on-axis; the purple line is forty five degrees off-axis. The lines in between are the angles in between.

You'll notice that the off-axis sound is *significantly* quieter. In the midrange it's down about 5db, it increased to 10db at 10khz, and at 20khz the off-axis sound is down fully 15db.

The red line is on-axis. At 1200hz there's a dip, then a peak at 1800hz, then another dip at 2400hz. This isn't thew waveguide; it's a reflection off the side windshield. That's why the peak and the dip are correlated in frequency.

Also, this measurement is with FIVE drives on one waveguide. You'll note that they're virtually indistinguishable in the graph. Compare it to the two-way, and you'll see what I mean. That's the Unity horn working it's magic.










If you look at the PDF that Andy posted, we're both on the same page. The off-axis sound is much lower in level, particularly at high frequencies.

Also, don't bother trying to do this with DSP; it can't be done. DSP can only fix things at one location. Move your head two inches and everything falls apart.

Here's the power response of the measurement from above.










Yes, I know that there's a hump from 3khz to 10khz :worried:

I've barely begun with the crossover, this is a very early version. It will continue to evolve.


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## dbiegel (Oct 15, 2006)

Patrick, I'm glad that you chimed in. I guess I misunderstood your goals looking at your earlier graphs in your thread which, at a quick glance, seemed to show almost identical levels on and off axis as being a great thing.. Apparently, I'm not the only one... A few people at Mr. Marvs brought this up and were trying to figure out ways to get their off-axis to be exactly the same as their on-axis.... ie the same level... I think I've seen a few people alluding to trying to do that in posts here as well. The more I thought about it, the less it made sense to me, so I figured I'd post about it and see if I'm out of my mind or if I just don't understand something.

So the idea is to have the off axis exactly the same as the on axis, just _attenuated._ That last part is the key, of course... If you had mentioned that in your graph discussions, I apologize for not reading carefully enough. I somehow got the impression you were trying to get the off axis exactly the same level too. Anyway, now it makes sense to me and I have a new appreciation for what you're doing! That makes it consistent with the reading Andy posted and what others have said as well. 

The question I have left is: how do you pull that off in the car environment? Even if you had the perfect speaker with the ideal, perfectly smooth off axis response -- there are people shopping around now for drivers with this perfect measurement -- won't the off axis still reflect differently at different angles and get absorbed differently anyway depending on the path it takes bouncing and diffusing around the car before it gets to your ear? Wouldn't you ideally actually want to take into account the different sound paths (reflections, diffractions, etc.) at each angle of off axis, and compensate for them with a waveguide having ridges, foam, and shaping in exactly the right places, or peaks and dips in the drivers' off axis responses to compensate (an unimaginably difficult task that somewhat boggles my mind just thinking about it)? In other words... wouldn't a driver that has perfectly flat off axis response measurements from the manufacturer might actually be far worse in a car than a driver with a couple big peaks and dips off axis, which you can then place to coincide with the peaks and dips caused when you put them in the car? Maybe this is part of why drivers that look good on paper can sound terrible once put in a car, and vice versa -- and why just moving a speaker around in a car to see what location sounds best before installing can be so beneficial?


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## dbiegel (Oct 15, 2006)

BigRed said:


> don't give up danny. i tried many things in my truck before settling on what I did. you'll get it.......keep experimenting bro
> 
> pm me if you're interested in the power supply for your processor


Thanks Jim... its a lot of fun to experiment with this stuff so I don't mind  I'm trying to decide whether to keep this processor or not, its kinda hard to justify investing another $150 into it (which seems to be what the supplies go for)... that would bring my total investment in it pretty close to bit one territory and I wouldn't have the crossovers... but if you have a cheaper source I'd love to know about it!


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## 14642 (May 19, 2008)

Hey Patrick,
It has and can be done with DSP--and a very specific arrangement of speakers. Here's a link to the explanation. I've heard this and it's amazing. 

http://www.xlrtechs.com/dbkeele.com/PDF/Keele%20(2007-09%20AES%20Preprint)-%20Linear%20Phase%20Digital%20Crossover%20Flters%20Part%202.pdf

BTW, Dr. Horbach is our principal DSP engineer and MS-8 is a result of some of his other work.


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## tspence73 (Oct 14, 2008)

Fast1one said:


> 3-way is a much better option but it can get expensive very fast with the processing, amplification, and driver cost. 2-way with full range driver just makes so much more sense on a budget and reduces complexity for beginners.


I see the point of this logic. It's not like 2-way is bad in any way. I agree that it will make it much easier on beginners to setup.


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## Patrick Bateman (Sep 11, 2006)

dbiegel said:


> Patrick, I'm glad that you chimed in. I guess I misunderstood your goals looking at your earlier graphs in your thread which, at a quick glance, seemed to show almost identical levels on and off axis as being a great thing..


Eek, that would be a very bad thing in the car. By focusing the sound into a beam, the way a flashlight focuses light, the waveguides create a solid center image. It also reduces the ratio of reflected to direct sound, which is something that Harman has been studying intensely, especially in the past few years. See D.B. Keele et al...



dbiegel said:


> Apparently, I'm not the only one... A few people at Mr. Marvs brought this up and were trying to figure out ways to get their off-axis to be exactly the same as their on-axis.... ie the same level... I think I've seen a few people alluding to trying to do that in posts here as well. The more I thought about it, the less it made sense to me, so I figured I'd post about it and see if I'm out of my mind or if I just don't understand something.
> 
> So the idea is to have the off axis exactly the same as the on axis, just _attenuated._ That last part is the key, of course... If you had mentioned that in your graph discussions, I apologize for not reading carefully enough. I somehow got the impression you were trying to get the off axis exactly the same level too. Anyway, now it makes sense to me and I have a new appreciation for what you're doing! That makes it consistent with the reading Andy posted and what others have said as well.


Yes I am definitely on the same page as Harman, and have a lot of respect for their research. Also the compression drivers in my previous car were JBL, and the compression driver in the new car is virtually identical to a JBL 2407H.



dbiegel said:


> The question I have left is: how do you pull that off in the car environment? Even if you had the perfect speaker with the ideal, perfectly smooth off axis response -- there are people shopping around now for drivers with this perfect measurement -- won't the off axis still reflect differently at different angles and get absorbed differently anyway depending on the path it takes bouncing and diffusing around the car before it gets to your ear? Wouldn't you ideally actually want to take into account the different sound paths (reflections, diffractions, etc.) at each angle of off axis, and compensate for them with a waveguide having ridges, foam, and shaping in exactly the right places, or peaks and dips in the drivers' off axis responses to compensate (an unimaginably difficult task that somewhat boggles my mind just thinking about it)?


Actually it's very easy! All you need to know is what your coverage angle is, and design a waveguide that covers it. That's it!

There's a lot of books and math on the subject, but when you get down to brass tacks, a waveguide is nothing more than a device which takes a wave and controls it's coverage angle. Nothing more and nothing less.

Note that I didn't say a SOUNDwave. There are waveguides for light, sound, radio, etc...

The dimensions of my waveguide are dictated by the dimensions of the waves I'm working with, which are between 1 and 46 inches in length.

I stole this pic off Lansing Heritage, it shows the difference between a horn and a waveguide. Note the waveguide's walls are basically flat.










dbiegel said:


> In other words... wouldn't a driver that has perfectly flat off axis response measurements from the manufacturer might actually be far worse in a car than a driver with a couple big peaks and dips off axis, which you can then place to coincide with the peaks and dips caused when you put them in the car? Maybe this is part of why drivers that look good on paper can sound terrible once put in a car, and vice versa -- and why just moving a speaker around in a car to see what location sounds best before installing can be so beneficial?


The on and off-axis response of any speaker is dictated by it's physical dimensions. You could measure a hundred woofers with similar dimensions, and their off axis response will be 90% identical. So trying to find a specific speaker with perfect off-axis response will generally lead you to the same place:

The speaker with the best off-axis response will be the smallest speaker.

Conversely, the speaker with the worst off-axis response will be the largest speaker.

In my last post, I showed the off-axis response of a five inch two-way, compared to my Unity. The Unity has five drivers, but it's off-axis response was better than the two-way. The reason why is that all five drivers are radiating from a point in space that's less than three inches in diameter. 

Here's a pic of a real Unity horn. The holes are for the midranges, and the tweeter is at the apex. All the sound is radiating from a point that's the size of a tennis ball.








That's the key to good on AND off axis response. The source of the sound has to be vanishingly small.

And of course, that's why tweeters have better off-axis response than woofers. They're small.


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## boltupright (Feb 14, 2007)

So if i wanted to limit off axis response I could have my midbass and midrange crossed over higher, like for example my 8" midbass from 60 - 800, and 4" midrange from about 800 - 5000?


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## tspence73 (Oct 14, 2008)

boltupright said:


> So if i wanted to limit off axis response I could have my midbass and midrange crossed over higher, like for example my 8" midbass from 60 - 800, and 4" midrange from about 800 - 5000?


Before you decide on your crossover plots, you will want to have a graph that shows the off-axis response and when it drops. Without that information, you would just be guessing. The general rule is that the larger the driver is, the sooner it's off-axis response will drop on the frequency graph. 

From my research so far I've noticed the following things. Smaller drivers tend to extend their good off-axis response to higher frequencies. Tweeters are the least predictable drivers and the off axis response can differ by thousands of cycles per second (some tweeters drop at like 8KHz and a few don't actually drop until like 15KHz). Midrange drivers vary slightly (it's usually based on size, smaller extends further) and woofers also have slight variances (size matters as well, smaller extends further).

The problem I've run into is designing a system that will be efficient (loud) and have great off-axis response. I initially was looking into trying to find maybe an XBL 4" mid that can maybe effectively get down to 300Hz yet still have low distortion/high SPL output. The Tang Band XBL tweeter delivers a perfect high range output level, low distortion, low frequency highpass capability. I'm now looking at what the perfect midrange would be. The reason for a 4" mid is that it's the driver size that seems most likely to be able to go down to 300Hz yet have good enough off-axis response to do a more ideal tweeter highpass of 2KHz - 2.5KHz. The more output capability and power handling capability the mid has, the better the odds that I will get a nice SPL output from the setup. 

Patrick Bateman seems to have the best solution in the Unity Horn design but it looks like enough of a pain in the ass to build and install in the dash that I will leave on the shelf as a last resort. I should have figured a waveguide or horn-based system would end up being the one that could deliver the best of both worlds.


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## Patrick Bateman (Sep 11, 2006)

boltupright said:


> So if i wanted to limit off axis response I could have my midbass and midrange crossed over higher, like for example my 8" midbass from 60 - 800, and 4" midrange from about 800 - 5000?


An eight inch woofer has a diaphragm that's about 6.5" in diameter, so it will begin to "beam" at 2076hz. (speed of sound / 6.5")

So unfortunately, no, that won't limit the off-axis response.

That's why I'm using the whole dash in my project. The wavelengths get ridiculous. 500hz is 27" long.


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## Patrick Bateman (Sep 11, 2006)

tspence73 said:


> Before you decide on your crossover plots, you will want to have a graph that shows the off-axis response and when it drops. Without that information, you would just be guessing. The general rule is that the larger the driver is, the sooner it's off-axis response will drop on the frequency graph.
> 
> From my research so far I've noticed the following things. Smaller drivers tend to extend their good off-axis response to higher frequencies. Tweeters are the least predictable drivers and the off axis response can differ by thousands of cycles per second (some tweeters drop at like 8KHz and a few don't actually drop until like 15KHz). Midrange drivers vary slightly (it's usually based on size, smaller extends further) and woofers also have slight variances (size matters as well, smaller extends further).
> 
> ...


It's tricky isn't it? LOL

If you want the off-axis response to be the same as the on-axis response, you have to get all the drivers really close together. We're talking within centimeters, even millimeters.

Here's some food for thought:

An Adire XBL 4" midrange has an efficiency of 85db or so. With 50 watts you'll get 92db out of it.

On the other hand, I can put a KCN5FD in a bandpass enclosure and get it's efficiency up to 100DB. That's with one watt. A pair will give you 120DB, with 100 watts.

More importantly, because the output is coming from a port, you can get all that output with an inch or two of your tweeter. I mean, it's difficult to get an eight inch woofer in your kick panels. But a pair of 5" woofer? That's a piece of cake, especially if they're buried inside of a box. Hell, mount them UNDER the dash. Just be sure the port is near the tweeter.

Remember, there's no reason you can't use a bandpass box for a MIDRANGE. Take a look at this picture below, and now imagine if it's a midrange instead of a sub, and the tweeter is located right next to the port.

And of course the dimansions would be very VERY small. The box size would be tiny. You could easily fit two 5" midranges into a bandpass box in the kick panels, along with a high power tweeter.


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## Patrick Bateman (Sep 11, 2006)

Andy Wehmeyer said:


> Hey Patrick,
> It has and can be done with DSP--and a very specific arrangement of speakers. Here's a link to the explanation. I've heard this and it's amazing.
> 
> http://www.xlrtechs.com/dbkeele.com/PDF/Keele%20(2007-09%20AES%20Preprint)-%20Linear%20Phase%20Digital%20Crossover%20Flters%20Part%202.pdf
> ...


Andy,

I've been studying horns and waveguides for almost fifteen years now, and the information in that paper is incredibly depressing.

Or it's the greatest thing I've ever read!

I can't decide which one LOL

Just skimmed through it on my lunch break, but if I'm understanding it correctly, we can control directivity on a FLAT baffle by using a very specific combination of crossover frequency and driver spacing.

That is absolutely HUGE.

If that is true, then it means that loudspeaker designers can use a modest waveguide to control the directivity of a tweeter, and mate it with a pair of woofers whose location and crossover point are chosen to yield a specific vertical beamwidth.

WOW

That could literally change the way speakers sound in rooms.

I have a set of uber-expensive constant directivity speakers at home, and they sound wonderful even with minimal room treatment. Sounds like JBL is on the verge of doing something similar with a flat baffle.


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## jaguardoc504 (Mar 25, 2009)

interesting


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## thehatedguy (May 4, 2007)

Andy, this MS-8 you mentioned...going to make it to market?


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## 14642 (May 19, 2008)

Yes.


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## Fast1one (Apr 6, 2007)

Andy Wehmeyer said:


> Yes.


I think thats the first time I have seen you say an absolute "yes"

Thats encouraging, I WILL be purchasing the unit upon arrival.


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## Patrick Bateman (Sep 11, 2006)

Patrick Bateman said:


> Andy,
> 
> I've been studying horns and waveguides for almost fifteen years now, and the information in that paper is incredibly depressing.
> 
> ...




After reading the paper that Andy posted, I was enthused to try out the ideas, so I put a simulation together.

It's basically a two-way, but flipped on it's side.

Picture something like this, but horizontal:








Here's a simulation of the polar response:








Please ignore the response above 5khz. This program cannot simulate waveguides, so we have to model them using an approximation. The results from 100hz to 5khz should be accurate.

Having said that, this is quite good performance! It's basically behaving as if we're using a waveguide that's twice as big!

How cool is that?

What you'll see in the graph is that the off-axis response begins to fall at 1khz, where it's about 3db down off-axis. That's like cutting the power by half. By 1800hz it's down almost 10db off-axis, which is like reducing the power by 90%. Remember, that's the key to good imaging and reducing the reflections. We have to narrow our beamwidth.

This could be particularly useful in a car, where it's very difficult to put your woofer and tweeter vertical, but it's easy to mount them horizontal.

If anyone has any questions about the sim, please let me know.

The sim is using a 6.5" waveguide mated to a woofer that's 5" to the left. The sim models vertical directivity, so I flipped the X and Y axis (so that it will model horizontally.)

The midrange is in a bandpass enclosure, and the output is coming from four ports with a diameter of 1/2". The ports are spaced 3.5" apart. This distance corresponds to one half wavelength at the crossover frequency.

That last part is the key. According to the paper that Andy posted, a distance of one half wavelength between the four sound sources creates a "cone of sound" with a coverage of ninety degrees. If you look at the simulation you'll see the output narrows dramatically at 2khz, just as the paper says.


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## western47 (Nov 17, 2008)

I haven't been following a lot of what has been going on around here lately but I will add my .02 sense. The recommendation of Toole's book is a great one. This is a reference if there has ever been one. Toole and Geddes are the pedestal guys if you ask me. 

It is very difficult if not impossible to achieve good imaging from multiple locations through the use of electronics. Using an acoustic solution such as a properly implemented waveguide seems to be the ultimate. I would also encourage others to look into multiple subs located throughout the cabin. Lastly, going to constrained layer dampening instead of mass loading for noise reduction is much more effective. Keep in mind that proper CLD techniques require and equally stiff panel using a mastik such as liquid nails for adhesion.

This is not my knowledge but some of the extremely important tips learned through the likes of Geddes and Toole. They are extremely useful in the home as well as car environment.


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## Gutbucket (Aug 20, 2009)

Very interesting thread.. subscribing to follow it further, thanks for the detailed write-up.


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## Chaos (Oct 27, 2005)

Subscribed.


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## Patrick Bateman (Sep 11, 2006)

western47 said:


> I haven't been following a lot of what has been going on around here lately but I will add my .02 sense. The recommendation of Toole's book is a great one. This is a reference if there has ever been one. Toole and Geddes are the pedestal guys if you ask me.


IAWTC. I work at home, and listen to a set of Geddes speakers at least eight hours every day. Love 'em.



western47 said:


> It is very difficult if not impossible to achieve good imaging from multiple locations through the use of electronics. Using an acoustic solution such as a properly implemented waveguide seems to be the ultimate. I would also encourage others to look into multiple subs located throughout the cabin. Lastly, going to constrained layer dampening instead of mass loading for noise reduction is much more effective. Keep in mind that proper CLD techniques require and equally stiff panel using a mastik such as liquid nails for adhesion.


Yeah, I tried to implement a speaker using the concepts that Andy posted above, but it didn't work out for me. It's not that it doesn't work (it does.) But the directivity narrows for about half an octave. So you have to use four or five drivers to implement it properly, and a big baffle. I was hoping you could do it with two or three, but no dice.

So it's back to horns for me. My latest project is here:

Creating a Soundstage with Waveguides and Psychoacoustics - diyAudio.com Forums










As for constrained layer damping, it works quite well. The tan goop all over this horn is an adhesive that's designed for subfloors. It costs $5 in a super-sized tube at Home Depot. As I understand it, the key is that the center layer remains flexible. That's why you want a subfloor adhesive. It stays flexible. If it didn't, floors would squeak when you walk on them. Also, I haven't applied the final layer of fiberglass.

One thing that's worked well for me is a layer of fiberglass, covered with subfloor adhesive. Once it dries I fill the gaps with clay, and then apply a final layer of fiberglass. The clay is required because the glue is lumpy. The clay fills the gaps.




western47 said:


> This is not my knowledge but some of the extremely important tips learned through the likes of Geddes and Toole. They are extremely useful in the home as well as car environment.


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## br85 (May 2, 2008)

Not to take away from the discussion of waveguides (which I am a big proponent of btw), but there is much more to crossing over a mid than just polar/power (on/off axis) and frequency response (power handling and displacement).

1. With most cone drivers worth their salt (at least somewhat pistonic), breakup nodes are going to be an issue before beaming is even considered. Since many of us run active without notch filters, it's silly to even bother considering polar response when crossing. Time is better spent finding the next driver up in the frequency range that can handle it down low. (or utilize waveguides)

2. Even on non-pistonic cones that sacrifice low end clarity for higher extending capabilities, the surround is likely to be the limiting factor (midrange driver). Even a 4" driver's surround has a horrible breakup/resonance of it's own, usually around 2 - 2.5khz. Why people can't hear this is beyond me. Maybe it's why that is the exact frequency range we often see the "audiophile dip". It even shows up on FR graphs, usually as something small. Measure the driver at 8 watts instead of 1 and it becomes painfully obvious.


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## Patrick Bateman (Sep 11, 2006)

br85 said:


> Not to take away from the discussion of waveguides (which I am a big proponent of btw), but there is much more to crossing over a mid than just polar/power (on/off axis) and frequency response (power handling and displacement).
> 
> 1. With most cone drivers worth their salt (at least somewhat pistonic), breakup nodes are going to be an issue before beaming is even considered. Since many of us run active without notch filters, it's silly to even bother considering polar response when crossing. Time is better spent finding the next driver up in the frequency range that can handle it down low. (or utilize waveguides)
> 
> 2. Even on non-pistonic cones that sacrifice low end clarity for higher extending capabilities, the surround is likely to be the limiting factor (midrange driver). Even a 4" driver's surround has a horrible breakup/resonance of it's own, usually around 2 - 2.5khz. Why people can't hear this is beyond me. Maybe it's why that is the exact frequency range we often see the "audiophile dip". It even shows up on FR graphs, usually as something small. Measure the driver at 8 watts instead of 1 and it becomes painfully obvious.


Admittedly I have OCD when it comes to directivity. I have spent a *month* trying to find the cause of a peak and a dip in my latest horns. I was convinced it had to be a reflection, since the car is such a reflective environment. I tried everything you could imagine:


Set up a temporary baffle around the speakers, in case it was reflecting off something
Stuffed foam blocks into the horn in case there was a reflection at the mouth
duct taped a foot of PVC pipe onto the horn, in case it was diffraction

Then I actually FELT the horn while it was playing, and it was buzzing.

Problem solved - the dip and the peak were due to a flimsy enclosure.

So I have to agree with you, it's hard to underestimate how much resonance can screw things up. Everything from cone break up to radiation from the surrond to vibrations in the baffle to resonances in the car itself.

Sometimes this hobby is a thankless p.i.t.a.


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## br85 (May 2, 2008)

I'd go so far as to say that structural resonance of all kinds is the absolute worst kind of distortion in every car "stereo" ever built. Makes me wonder why paying big dollars for super clean amps and drivers worth thousands is even somewhat acceptable in this hobby.


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## tspence73 (Oct 14, 2008)

br85 said:


> I'd go so far as to say that structural resonance of all kinds is the absolute worst kind of distortion in every car "stereo" ever built. Makes me wonder why paying big dollars for super clean amps and drivers worth thousands is even somewhat acceptable in this hobby.


I agree here. I think if anyone is truly serious about sound quality and hi fidelity in a car, then sound deadening & cabin isolation is required. 

It's simply fricken retarded to even think about high-end equipment if car acoustics aren't HEAVILY treated first. EVEN THEN it's still arguable that there is no amount of sound isolation materials which will make enough of a reduction in noise to justify buying high end gear. If you're unable to hear the difference due to ambient noises, then it's pointless beyond a certain level of quality/low noise.


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## Patrick Bateman (Sep 11, 2006)

tspence73 said:


> I agree here. I think if anyone is truly serious about sound quality and hi fidelity in a car, then sound deadening & cabin isolation is required.
> 
> It's simply fricken retarded to even think about high-end equipment if car acoustics aren't HEAVILY treated first. EVEN THEN it's still arguable that there is no amount of sound isolation materials which will make enough of a reduction in noise to justify buying high end gear. If you're unable to hear the difference due to ambient noises, then it's pointless beyond a certain level of quality/low noise.


Not true.

I'm too busy at work right now to dig out the studies, but there have been numerous articles on psychoacoustics which demonstrate that we're *very* sensitive to the first few milliseconds of sound. After that, our brain just "merges" everything together.

That's why the other poster is so correct; resonances in the speaker, the baffle, and close to the driver are paramount, because they interfere with that first few ms of sound.

Putting my money where my mouth is, I haven't applied a single ounce of sound deadening to my 2nd car. My first car is *extensively* treated; the doors, roof, floor, trunk, etc...

IMHO, it was a waste of time and money. I would discourage anyone from doing it. If you want a quiet car, BUY a quiet car. Car and Driver publishes ambient sound levels for all the cars they review.


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## Patrick Bateman (Sep 11, 2006)

dbiegel said:


> I've noticed lately that there's a new "forum boner" myth of sorts emerging: that off-axis response should mirror on-axis response. It seems to have begun in the discussion of Patrick Bateman's awesome unity waveguide project...
> 
> So anyway, I'm not meaning to be a jerk or anything, but I guess I just don't get where this off axis should mirror on axis concept came from. Intuitively, it doesn't make sense to me and in fact goes against much of what I've researched, experienced, and experimented with in a car (though it makes some sense to me for a home or studio). Am I the only one who feels this way?
> 
> Maybe I'm just confused and I will certainly try to keep an open mind. I'd love it if someone could either explain to me the theory of why this is beneficial in a car, and/or point me to some white papers etc that back this theory up.


Dude, don't you OWN constant directivity waveguides? IIRC, you're running Image Dynamics right?

I smell "shenanigans"


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## HonorsDaddy (Aug 22, 2009)

Very interesting thread....made joining worth it all by itself..


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## br85 (May 2, 2008)

The other thing that car audio nuts are guilty of is ignoring baffle and step response. As if their drivers are going to reproduce anything like what they're supposed to when baffles are not even considered important.

The reason people like PB and myself go on and on and on and on and on about waveguides is because they're the OBVIOUS solution to acoustic diffraction on a tweeter. A waveguide is simply an inverted baffle, increases low end output and when built and integrated smoothly, prevents brick-wall type dips and peaks which cannot be fixed. Any peaks caused by a smooth waveguide will be of a somewhat smooth (although maybe quite heavy) effect.


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