# A brief look at excursion vs. frequency of various speaker sizes



## mvw2 (Oct 2, 2005)

I have two graphs for you guys. One shows common woofer sizes, 5.25", 6.5", a larger 8" woofer, and a 12" subwoofer. The other shows common tweeter sizes, 3/4", 1", and a 2" full range thrown in for good measure.


















Although subwoofers offer a good amount of excursion, midrange woofers and tweeters do lack considerably. Most midrange woofers have excursion levels in the 3mm to 6mm range. Most tweeters only have about 1mm of clean excursion.

The above graphs show necessary excursion levels of a speaker of each size in order to output 100dB at a distance of 1 meter. The numbers are actually a little generous as I did not use equivalent cone area but rather just 1" tweeter = 1" usable diameter just to be easy. The level of generosity varies a bit from something like the small 3/4" tweeter to the large 12" woofer. I'm showing this as more of a relative comparison rather than true numbers.

The key to this little experiment is to show how much excursion or how big of a speaker do I need to play loud. It also illustrates where the common weakness is in a system. Where _are_ your crossover points and where _should_ they be? When you have a common component set consisting of a 1" tweeter and a 6.5" woofer, you must expect certain limitations. Generally this is excursion. These graphs answer questions like why does my tweeter sound harsh when I play at high volumes or why does my woofer bottom out. Why do people prefer 6.5" woofers over 5.25" woofers. How different is the usability?

There's more to it than this. For example, there's the natural frequency response of the speaker or issues with distortion above or below a certain frequency. Subwoofers have enclosures that help shape and control frequency response and excursion use(especially ported).


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## T3mpest (Dec 25, 2005)

mvw2 said:


> I have two graphs for you guys. One shows common woofer sizes, 5.25", 6.5", a larger 8" woofer, and a 12" subwoofer. The other shows common tweeter sizes, 3/4", 1", and a 2" full range thrown in for good measure.
> 
> 
> 
> ...


One thing I like about this graph is that it shows the true key to actual midbass output is high effeciency as excursion is pretty low for a 8inch driver from 80-250hz.


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## ~thematt~ (Sep 14, 2007)

Nice graph. One thing you might want to add is reference scales (ie dB(A) dB(B) dB(C) etc. etc.) that way, you'll understand the difference a bit more, seeing as 100dB at 2-3kHz will start you're ears slowly bleeding (because we are most sensitive here), whereas 100dB at 20Hz is barely enough to lift one's skirt.


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## Abmolech (Nov 2, 2006)

> One thing I like about this graph is that it shows the true key to actual midbass output is high effeciency as excursion is pretty low for a 8inch driver from 80-250hz.


Hooray someone gets it. 

Unless your using arrays and /or wave guides, 6.5 " and 5 1/4 " drivers are never going to cut the grade in a moving vehicle.

This is why I pay NO attention to car competitions.
IE I use my system in a moving vehicle.

Great post, however some cravats..

This would be at how many steradians? 
Is this using a proper baffle (blocker) that separates the front form the rear wave?
Does this use acoustic loading in an enclosure to gain 3 dB, or is this lost to heat?


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## tcguy85 (Oct 29, 2007)

~thematt~ said:


> seeing as 100dB at 2-3kHz will start you're ears slowly bleeding


is that really true or an exaggeration.


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## GlasSman (Nov 14, 2006)

Nice graph.


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## mvw2 (Oct 2, 2005)

We do perceive different frequencies at different levels. You could say measured flat isn't human flat.

I just picked 100dB as a simple point, something that is relatively loud. The formula doesn't take into account any effects, not baffle, not off-axis, not anything really, just simple SPL at X distance via Y volume movement(cone area and excursion). It's not that complex, and it's not meant to be.

I must say, this is the first time I ever seen the term steradian used before.


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## Dangerranger (Apr 12, 2006)

Doubling the drivers and power will give a rough 6db increase, cutting necessary excursion in half. That's about the only way you'll get loud and low cleanly with 7" drivers


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## cvjoint (Mar 10, 2006)

I appreciate the effort...this is a very rewarding thread. Is there a way to add a 10 on there and check all at 110db for comparative reasons


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## DonovanM (Nov 1, 2006)

For some reason my comcast does not like your gigafiles site... this is the 2nd time I haven't been able to see your pics. I wonder why


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## Abmolech (Nov 2, 2006)

> Doubling the drivers and power will give a rough 6db increase, cutting necessary excursion in half. That's about the only way you'll get loud and low cleanly with 7" drivers


While I appreciate your sediments to the use of array's, and there under use in car audio, it is not the only way.

The above graphic example assumes free air and a frequency band width below room modal axis. 

For example 
By using a sealed enclosure it is quite possible to reduce the excursion, because the rear wave acoustic impedance is increased, and therefore a 3 dB amplitude lift can be realised where the acoustic impedance is sufficient to do so. (read 50 - 80 Hz), a reflex enclosure can use a helm holtz resonator to increase this further, however at the expense of a steeper roll-off curve. (12 degrees for a sealed versus 24 for a reflex, or extend it even further with a passive radiator to 29 degrees)

2PI steradians would give a 6 dB increase in acoustic output. (read wave guide), a 4 PI steradians load would give a 12 dB increase, and is responsible for you sub bass transfer. 

Welcome to the real world of car audio.

Where large woofers, array's, wave guides and horns reign supreme.


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## Oliver (Jun 25, 2007)

The highpass x-over of a driver based on the mechanical x-cursion was very nicely illustrated in the graphs [ this is why you cannot play your drivers at a high enough volume to satisfy yourself ], IB ,they crackle or pop when most Turn-it-up !  

If not downright bottom-out ! Think slim mount speakers , no bumped backplate, etc..,


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## fhl (Sep 20, 2006)

mvw2 said:


> We do perceive different frequencies at different levels. You could say measured flat isn't human flat.


Equal-loudness contour.

Frode


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## MarkZ (Dec 5, 2005)

Me likey.

What are the y units? mm?


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## mvw2 (Oct 2, 2005)

Yeah millimeters.


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## durwood (Mar 7, 2007)

This is a great extension of your older thread.


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## mvw2 (Oct 2, 2005)

A different approach and a different purpose. 

By the way, the other thread he was referring to:
http://www.diymobileaudio.com/forum/showthread.php?t=9094

Basically I just got my W18NX woofers, had my Alpine tweeters(Scan 6000) and I was fiddling around with what kind of excursion/thermal limitations I was working with. With the equation I used for this example and another one I found relating SPL to sensitivity and wattage(using the published frequency response chart), I sort of build a "capability chart" for the W18NX woofer, indicating the thermal limits, excursion limited, and even expected cabin gain using a basic 12dB/oct boost from 80Hz on down. It was a neat experiment and it could be applied to any woofer, tweeter, or even a component setup. You could even apply equations to account for crossovers or EQing.

This thread is more specific to the question why do I need 12mm Xmax in a 6.5" woofer or need to step to an 8" woofer to play down to 60Hz? It's a "bound by the laws of physics" thing. I'm not trying to be dead-on accurate, just more of an educational (theoretical) example. I do agree there are (many) other factors that come into play in the real world that one should account for or at least think about when designing their audio system and choosing hardware.


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## mosca (Oct 26, 2009)

sorry to refloat this four year thread, but the graph isn't showing anymore. would somebody upload it please?


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## amungal (Mar 29, 2010)

Interesting stuff. Now where's that graph?


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## cvjoint (Mar 10, 2006)

as a bump: I am pretty sad to see a lot of the old threads without any pic support, I'm not sure if it's a technical issue or not, especially since the oldies are goldies haha


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