Science Questions

How does a single speaker play many simultaneous frequencies?

Sun, 5th Jun 2011

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Dominic Parker asked:

I've been an avid listener for only the past month or so when I've been listening to the podcasts on my walk to and from the library everyday to revise, and am absolutely loving it so far and have managed to get through a good 30 or 40 of the latest podcasts in this short period of time... Anyway just a few things I was wondering if you could help me with:


As an amateur musician and DJ I have forever struggled to work out how it is that, particular in cheaper more basic speakers, a single speaker cone/diaphragm is able to vibrate at so many different frequencies at any one time in order to produce the full tonal frequencies of a piece of music? So essentially: how is it that it is able to recreate a kick drum at say 70Hz whilst still producing a clear strings note of 1700Hz undisturbed.



Thanks very much for your time


Dom Parker


Dave -   If the speaker was to produce a single frequency, think what that actually means - it means that the speaker is moving backwards and forwards, and causing the air to move backwards and forwards in a sin wave pattern.  You've probably seen a sin wave.  Itís basically just a very specific zigzaggy wiggly line.  Now, if the speaker moves in any other pattern than that, you could imagine itís moving slowly with a big wiggle and then on top of that superimposed, there's a little wiggle.  So, moving in and out slowly but on top of that is kind of vibrating a little bit.  So then it would be outputting sound with the low frequency, the big slow wiggle, and also a much higher frequency as well, at the same time.   The way that sound works is you can superimpose the motion of the speaker, you can superimpose lots and lots of different vibrations and that will produce sounds of lots and lots of different frequencies, all at the same time by just making the right pattern for the speaker to move back and forwards.  Itís not moving in a smooth wiggle, itís doing something incredibly complicated and that's a mixture of lots of different frequencies.


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It's all due to sound being a wave.  When you have waves coming from multiple instruments, all you have to do to get the total sound wave is to add them all up on top of each other.  The resulting wave looks pretty ugly (there's a gallery of some here:, but it's got all the information about what instruments play when, since they're all in there added up together.  This wave would be what hits your ear and lets you hear the music if it's being played live.

All a speaker has to do is to recreate that wave so that it comes from the speaker and hits your ear.  Then it sounds like whatever was recorded.  To do that, it just has to vibrate in time along with that complicated looking wave.  jpetruccelli, Thu, 2nd Jun 2011

Unfortunately, there are also subtle problems with trying to do this using a speaker. It works very well but even a theoretically "perfect" speaker also introduces some distortion. One of the main distortion products is intermodulation distortion. This results from having the combinations of frequencies present. A low frequency tone will be moving the cone back and forth and any high frequency tone is then "frequency modulated" by the lower tone because of the Doppler effect from the moving cone. This is minimised by having multiple speakers (also helpful in other ways) but this is a fundamental limitation to speaker quality. Earphones suffer very little from this because the movement of the tiny cone is very small as the power is so low, whereas high power speakers, with neoprene supported cones, have a long movements and will introduce distortion unless multiple speakers are employed.

There are some speakers that have a feedback system to correct this but it only works to some extent because of other limitations. There are also some very unusual designs that can avoid it but only at the higher frequency bands (Fane Ionophone). Large area speakers, multiple units or use at low powers minimises the problem and, as I said, earphones hardly have it at all.

Having said all this, speakers are actually pretty good and what JP said is correct. I thought I would just elaborate a bit :-) graham.d, Thu, 2nd Jun 2011

As they work a bit like speakers in reverse, do our eardrums cancel out some of intermodulation? Geezer, Thu, 2nd Jun 2011

Unfortuantely they don't. This would only be the case if the ear drum was mechanically coupled to the speaker so that the speaker movement and eardrum movement was identical. This is much closer to being the case with an earphone.  graham.d, Fri, 3rd Jun 2011

But doesn't the air, at least to some extent, mechanically couple the speaker cone to the eardrum? Geezer, Fri, 3rd Jun 2011

If in an enclosed environment (like the ear with an earphone shoved in it) and where the distance is less than the shortest wavelength, it is pretty good. Not with speakers though. When listening to live music from individual sound sources, the ear receives each sound as simple superpositioned waves. The movement of the receiving diaghragm is tiny. When this is all being sent from a single speaker cone there is non-linear mixing of the signals as can be understood from just two tones - a low one and a high one as described previously. The low tone will Frequency Modulate the high tone because of the Doppler effect. The Fane Ionophone (if it is still made) gets around this by having a continuous stream of air coming out which has its flow modulated by the signal. This does not produce IM distortion but regettably will (I expect) produce a slight hiss from the air stream. The simplest trick is to have multiple units and reduce cone speeds by having a large diameter for low frequency units. graham.d, Fri, 3rd Jun 2011

Right, no disagreement there Graham. What I'm wondering though, while the displacement of the eardrum is very small, isn't it still susceptible to a certain amount of intermodulation?

Presumably the excursion of the eardrum is rather large in response to a loud bass tone and a treble tone will still be superimposed as a simultaneous high frequency excursion. Mind you, I don't know squat about eardrums, so I'm making some big assumptions here. Geezer, Fri, 3rd Jun 2011

Yes, you are correct, but the movement is very small, and the velocity low compared with the speed of sound. The intermodulation effect is negligible compared with a typical speaker cone.

Although this IM distortion in speakers is significant, measurable and, more to the point, noticeable, most people accept it. It is really Hi-Fi nerds (and ex-hi-fi nerds like me) who worry about such things. It is probably one of the largest distortion contributors in a music play-back system but the concentration is always directed to the easily measurable and controllable performance of the electronics. I won't go into the selling of gold plated connectors etc. :-)

graham.d, Sat, 4th Jun 2011

Thanks Graham. I think I get it now  .

On small things like an eardrum, because the deflection at a given frequency is small, the velocity is also small. As the size of the transducer increases, this effect is "amplified" ( ), so the velocity of the cone in a large speaker, even at a lowish frequency, can actually be great enough to produce a significant Doppler effect.

Velocities sufficient to produce similar intermodulation with small transducers will only occur at significantly higher frequencies, and those frequencies are probably beyond the range of the transducer and human hearing. Geezer, Sat, 4th Jun 2011

A speaker is not made like a piano or pipe organ.

The piano or organ makes "pure sounds", such as A, B, C, etc with each string or pipe playing a single note.  And, each one creating an independent sinusoidal sound wave.  Put them together and you get a symphony.

On the other hand, a microphone picks up vibrations, but perhaps is better thought of picking up relative displacements of a diaphragm. 

The speaker then reproduces this relative displacement of the diaphragm independent of the original "notes" that had created the sound. CliffordK, Sat, 4th Jun 2011

Interesting that it should be said that distortion rises from the doppler effect of the speaker cone, on low frequencies, shifting the high frequencies in what must be an FM manner. Technically, that would have to occur. However, if that is significant, is it not also so that when live instruments play, a strong low-pitched instrument, by distorting the velocity of air in the vicinity of a higher pitched instrument, will have the same effect?  As for causes of distortion, I had been under the impression that the biggest causes of distortion in speakers was first of all non-linearity in its deflection compared to the input current, and secondly, resonances in the speaker or its enclosure, and if you get rid of those two problems, you will have a very good sounding speaker. Atomic-S, Mon, 6th Jun 2011

I'm sure there must be some amount of intermodulation between instruments, but the great thing is (at least for those electronic engineers involved in designing the ultimate in hi-fi) you can't call it distortion  Geezer, Mon, 6th Jun 2011

Atomic-S, I don't think that it is the case that the presence of a nearby instrument distorts the sound of another, at least via Doppler effect as described, but I have not done any maths to prove this; I think the waves superpose without intermodulation. What does happen is that instuments themselves do not produce sine waves (as Clifford suggests) but rather complex sets of harmonics; these often share a common resonance chamber whose walls vibrate in sympathy with the notes generated. I think it is in the art of instrument manufacture that the overall effect sounds "good" whatever the distortion components added. In this case the "distortion" is not regarded as such, as Geezer says. The sound reproduction system must simply not change this sound by adding to the distortion. Instruments could cause other instruments to vibrate, which could influence their sound I expect, but again this is something that we would tolerate and I think the effect would be relatively small in terms of IM distortion. One issue of electric pianos is that they do not model the sympathetic vibrations of "undamped" strings.

You are right Atomic-S that there are other forms of distortion in speakers. Speaker manufacturers (like all the other Hi-Fi makers) make a big issue about how they fixed the problems that they can fix but tend to keep quiet about the ones they can't (at least not easily). Flatness of frequency response is actually not very important to listening quality within fairly large limits but this is usually shouted about quite a bit. Speaker enclosure resonances have been tackled quite well with good speaker systems. Ironically a lot of people like a booming bass (OK for some music) so they actually like a bit of low frequency resonance. Note that the modern trend to have a separate sub-woofer is is good on many counts, including reduction in IM distortion. Phase distortion (variation with frequency) can make some measured results look terrible but the ear is almost completely immune to such distortion. Non-linear deflection vs input current would indeed create a lot of odd-harmonics but speaker design has reduced this so that it is only a problem if the speaker is overloaded. Another issue is the lack of stiffness of the diaphragm which can have its own resonances. Again modern materials have improved this.

Note you won't find much discussion about IM distortion in speakers though. The only easy (partial) solution is multiple speaker units and not driving them too hard. The problem, and many other distortion issues, are solved by use of earphones (and to a slightly lesser extent by headphones), but this is not so acceptable in terms of a proper stereo image and/or having a "shared experience" with other listeners.

But, hey, just listen to the music and don't worry so much about reproduction quality. As I've got older I've found my my ears add distortion with loud music so what's the point :-) graham.d, Mon, 6th Jun 2011

I think these gents sum the situation up quite well Geezer, Mon, 6th Jun 2011

I hadn't really thought of that!  You can download a set of ringtones from apple which can be used to estimate age ( ie under 16s can hear A, under 20s B etc) - my brother (a teacher) has actually noticed them in use .  So you have men of certain age spending frankly ludicrous amounts of money on hi-fi equipment - only to listen to it with lo-fi ears.

And yes this is the pot calling the kettle black; I was the proud owner of a valve amplifier/dock for my iphone (till some scrote nicked it) - very silly and a waste of money but great fun and a real work of art! imatfaal, Mon, 6th Jun 2011

I can't say I miss the sound that valve amps produce much, by I do miss the aroma of a hot valve amplifier! I wonder what I was inhaling - probably a lethal cocktail of things long since banned. Geezer, Mon, 6th Jun 2011

When I was 16 I could hear the 20kHz whistle from a TV line output transformer running on the French 819 line system, now I am hard put to hear a 4kHz tone. syhprum, Tue, 7th Jun 2011

Actually my ears' frequency response is still quite good but I do hear some unpleasant distortion at high volumes even with live concerts. I was blaming it on poor stage reproduction equipment until I noticed it with an unamplified choir! I have also noticed I can't hear people as well (can't pick out their words) in noisy situations but I think that may be something in the brain as much as in the mechanics of the ear. My wife has a similar problem.

On a similar subject, why do cinemas feel the need to have the sound volume at ear-knackering high levels? Maybe it to drown the sound of all the noisy food and food packaging they sell. I sometimes end up using earplugs. graham.d, Tue, 7th Jun 2011

I can't imagine Star Wars opening with elevator music!!!

And big images go with big sounds.

But, I certainly have never been attracted to sitting in the front rows. CliffordK, Tue, 7th Jun 2011

Dominic Parker asked the Naked Scientists: As an amateur musician and DJ I have forever struggled to work out how it is that, particular in cheaper more basic speakers, a single speaker cone/diaphragm is able to vibrate at so many different frequencies at any one time in order to produce the full tonal frequencies of a piece of music? So essentially: how is it that it is able to recreate a kick drum at say 70Hz whilst still producing a clear strings note of 1700Hz undisturbed. Thanks very much for your time Dom Parker What do you think? Dominic Parker , Tue, 7th Jun 2011

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