# How Speakers Handle Multiple Frequencies Simultaneously



## TCSProducts (Jul 29, 2010)

There was some discussion in another forum this week about how speakers work, and how they handle multiple frequencies at the same time. I figured I’d clean this up and re-post this here where it belongs. 

*Assumptions*:
You know what a Sine Wave is
You know that mathematically, a sound wave is a Sine Wave
You know how to read a 2-D, X-Y graph
You know how a speaker works


A few basic definitions:
*Frequency*: Speed of the wave oscillation in cycles per second (Hz) for a complete wave cycle (zero -> high peak in positive direction -> cross zero -> low peak in negative direction -> back to zero). For our application, Frequency is the pitch of the sound we hear.

*Amplitude*: The strength of the wave, measured in whatever units we’re measuring (Volts in our case, but can be decibels, psi, or whatever). This correlates to the Volume (loudness) of the sound from the speakers.


Here is a plot of a simple sound wave; the frequency (5 Hz) is in the X-direction and the amplitude (10) is in the Y-direction:











Note that this is a Mathematical Function – that means that there can only be *ONE* Y-value for each X-value on the graph. If there is more than one Y-value at any given instant, then there is more than one signal. 

Also note that a single speaker can only reproduce *ONE* signal, so a speaker cannot actually reproduce multiple frequencies at the same time. The following plot of 3 distinct waves is *NOT* a mathematical function and *CANNOT* be reproduced by a single speaker, because there are three Y-values for each X-value:









10sin(31.5x) (Black line); 5sin(12x) (Red line); 12sin(6x) (Blue line)


In reality, we know that music is comprised of more than one single pure signal, and to understand how it gets to a speaker we need to have a basic understanding of sound recording and processing. When a band records a song, for example, each instrument or voice is recorded on its own single track. The individual tracks are then combined, along with editing and effects, to produce the final product. 

That resulting waveform is actually the *SUM* of all of the waveforms of the individual tracks, including their respective frequencies and amplitudes. When multiple tracks are combined, the phenomenon of *Wave Interference* takes place, where the Y-vales of the waves are simply added together to produce a resultant waveform. Here’s how it looks:









10sin(31.5x)+5sin(12x)+12sin(6x) (Green line)

If you look at any X-point on the graph, simply add the Y-values at that point and that’s the final value (green line) at that instant. 

Here’s what the cleaned-up final wave looks like after adding the waveforms. The resultant composite waveform contains changing frequency and amplitude characteristics to incorporate the original information:










This is the final signal that gets put on the CD, and that your head unit reads. Your stereo does some other tricks like frequency filtering, digital to analog conversion, stereo decoding, and other stuff to manage the signal, but those are entirely different subjects. In the end, only one composite signal gets sent to each speaker. 

Now you might be wondering what happened to the other 3 waves – where did they go, and where is the information they contained? Well, you’re looking right at it – all 3 waves are still there and none of their information is lost – just look at the big picture:









Signal 1, overlaid on final waveform










Signal 2, overlaid on final waveform










Signal 3, overlaid on final waveform


As you can see in the above plots, each of the 3 original waves is still there, at the correct frequency and amplitude. Remember that your speaker only reproduces the final waveform, but the single final waveform includes all of the information from the original waves. From your speakers, you will hear each distinct wave simultaneously, each at its respective pitch (frequency) and loudness (amplitude).


Just imagine how the final waveform might look with a few hundred separate waves summed together, with each wave constantly changing frequency and amplitude, with all the harmonics, background noise, added effects, and processing. Things can end up pretty messy. What that means here is that the “best” equipment is more capable of reproducing that final signal accurately – filtering and crossovers, speaker and amplifier design, internal vehicle acoustics, and a whole list of other variables all affect how that signal sounds to your ears.

Questions and further discussion are always welcome...



Thanks to FooPlot for easy function plotting.


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## mattphelps (Dec 12, 2010)

Speakers work by the frequency produced by the sound. The frequency received by the speakers is then interprets the music, thus producing sound. The driver produces sound waves by rapidly vibrating the cone.


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## tornaido_3927 (Nov 23, 2009)

mattphelps said:


> Speakers work by the frequency produced by the sound. The frequency received by the speakers is then interprets the music, thus producing sound. The driver produces sound waves by rapidly vibrating the cone.


...Na man. :laugh:

A speaker simultaneously reproducing different frequencies blew my mind when I first got into audio, I had no idea how that happened. Even though I've been educated since then, this is a good and informative post, cheers


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## pat_smith1969 (Feb 17, 2010)

Hey... I started that original post on the other forum.. yeah me!!!

This was a GREAT write up. Very clear and well presented with just enough graphs to get your point across. Thank you. (I would give you an A+ if I were handing out grades).


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## Jaredturp (Apr 30, 2010)

Wonderful and informative post. Both my father and I have always tossed this question back and forth and this clarifies it beautifully. Thanks!

I guess my only question is whether there is a great loss in quality when all the signals are added together? It would seem so based off how great the graphs differ from the resulting signal. Especially the "Signal 2, overlaid on final waveform" graph.


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## Oliver (Jun 25, 2007)

Jaredturp said:


> I guess my only question is whether there is a great loss in quality when all the signals are added together?


It's better than no speakers.

Breaking down the frequency spectrum and assigning certain frequencies to certain drivers has given me the most listening enjoyment!


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## Jaredturp (Apr 30, 2010)

Oliver said:


> It's better than no speakers.
> 
> Breaking down the frequency spectrum and assigning certain frequencies to certain drivers has given me the most listening enjoyment!


But even when you split between frequencies, there are still multiple instruments creating each frequency and then adding in harmonics right?.... music is too complicated!!


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## Oliver (Jun 25, 2007)

Bose 141 Pair Fullrange Bookshelf Speakers

* Compact Size and Classic Style
* High-Quality Sound
* Clearer, Deeper Low Notes
* 10 to 80 Watts
* 4 to 8 Ohms




> A full-range loudspeaker drive unit is defined as a driver which reproduces as much of the audible frequency range as possible, within the limitations imposed by the physical constraints of a specific design. This is so difficult that there are few manufacturers producing full range drivers for high fidelity use


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## TCSProducts (Jul 29, 2010)

Jaredturp said:


> Wonderful and informative post. Both my father and I have always tossed this question back and forth and this clarifies it beautifully. Thanks!
> 
> I guess my only question is whether there is a great loss in quality when all the signals are added together? It would seem so based off how great the graphs differ from the resulting signal. Especially the "Signal 2, overlaid on final waveform" graph.


The second signal is still there - if you look closely, it appears as the average of a pair (or maybe triplet) of the highest frequency wave cycles.

The ideal solution, of course, would be to have an infinite number of speakers, each reproducing a single wave, which would combine to recreate the original source perfectly - but that's not very practical...


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## tornaido_3927 (Nov 23, 2009)

I think the biggest killer with multiple simultaneous frequencies would be intermodulation distortion, wouldn't it? Not including of course trying to play an 80hz and 3000hz wave at the same time through a 3 inch driver..





TCSProducts said:


> The second signal is still there - if you look closely, it appears as the average of a pair (or maybe triplet) of the highest frequency wave cycles.
> 
> The ideal solution, of course, would be to have an infinite number of speakers, each reproducing a single wave, which would combine to recreate the original source perfectly - but that's not very practical...


Dammit I wanna see someone try this


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## pjhabit (Aug 12, 2008)

tornaido_3927 said:


> I think the biggest killer with multiple simultaneous frequencies would be intermodulation distortion, wouldn't it?


Multiple sources (w/ multiple PLDs) playing the same signal, can create some nasty comb filtering.


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## NSTar (Feb 24, 2010)

I have 20 speakers coming from one channel...all split at 48db per 1k frequencies, using chained mini dsp. 

all level matched.

dont neee crazy expensive speakers either lol


someday..when I have time


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## tornaido_3927 (Nov 23, 2009)

pjhabit said:


> Multiple sources (w/ multiple PLDs) playing the same signal, can create some nasty comb filtering.


Yeah true, but I was talking from a single driving playing multiple frequencies..


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## tibug (Jan 22, 2011)

Very interesting and well put together! 

I'm selling my whole system and buying some tickets to a live concert. Much cheaper than trying to accurately reproduce sound inside of a car.


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## Jaredturp (Apr 30, 2010)

I love concerts as much as the next guy, but a night of awesome music doesn't really compare to being able to listen to quality music every day.


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