I am trying to understand what happens when two or multiple sound waves meet up or clash into one and another.

An example: Lets say I play middle C on the piano and a C an octave higher on the guitar at the same time, does these two sound waves merge and become one big complex sound wave or do they interact in another way?

Are there multiple ways/types of interactions sound waves can have depending on if I play the notes at the same time or not?

I am interested in the acoustics of this question


When two soundwaves play at the same time, nothing very complicated happens - they just get added together:

piano and snare

In this picture, the first track is a snare sound; the second is a piano sound; and the third is a picture of the mixed sound. All that has happened is that the level of the snare wave at every point has been added to the level of the piano wave at every point.

So, if they're mixed together like this, how can the ear still identify both sounds?

The reason is that the ear analyses things in the frequency domain. let's have a look at what that looks like:

frequency domain

that's a bit of a rough picture - I'm sure someone can do a better one. But on the first (snare) track, you can clearly see that the sound consists of broadband noise, across most of the frequency spectrum, while on the second (piano) track, you can clearly see the horizontal lines representing the harmonics of the note. If you look at the third (mixed) track, you can make out both - the harmonics of the note first, and also the area of broadband noise when the snare hits. So here we can tell 'by eye' that both sounds are happening, and that's more or less the trick the ear uses too.

Of course there are occasions when the presence of one sound affects the perception of another. This is known as masking.

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  • This is in many ways equivalente to what happens to visible light when different light sources get mixed up. The difference is that, while the ear is way more simple than the eye, so you can hear far less "sound pixels" than what your eyes can detect regarding color and light. – T. Sar Apr 2 '18 at 19:45
  • @T.Sar - yes, but you can detect orders of magnitudes more different wavelengths... – Jules Apr 2 '18 at 21:59
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    @user1886419 it really is ADDing. It might not look like it because the peaks on these waveforms don't coincide or because we're not very zoomed in. – topo Reinstate Monica Apr 3 '18 at 5:34
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    @topomorto Also, it's adding in linear terms, whilst I assume the display is in dB (logarithmic). So it will appear to be a smaller change. – endorph Apr 3 '18 at 5:51
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    @CarlWitthoft it sounds like you're talking about a different 'waveform' to me - perhaps some kind of 'waveform' of average power (e.g. RMS averaged over a window)? I'm simply talking about the 'actual' waveform of sound pressure (or voltage, or digital values). What I said about those waves simply 'adding' pointwise is the very reason why you get the effect you describe - when you add a negative to a positive, the result is a subtraction, so two similar waves with out of phase with each other will cancel. – topo Reinstate Monica Apr 3 '18 at 13:50

Yes. At your ear there can be only one momentary air pressure. The values of this through time can be represented as a very complex waveform - which our brains can be very good at analysing as several distinct instruments. (Our brains can also be easily fooled!)

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    Strangely enough :-) , this is the exact correct answer. As to how the particular pressure vs. time function is produced, refer back to portions of topomorto's answer and my comment there. – Carl Witthoft Apr 3 '18 at 13:16
  • If I understand correctly, the cochlea transforms the impulses from the air pressure in the ear into various separate frequency components, and then the brain starts from those separate frequency components. – ninjalj Apr 3 '18 at 16:11

I asked myself the same question several time, and frankly the answers I see here would have only partially satisfied my curiosity (topomorto's one being the one that gets closer to that), so I will try to add my two cents and make it more and more complex at each stem

1 ] Generally speaking, and with some degree of approximation, yes: sound waves "merge" into a more complex sound wave and nothing special happens, as the resulting wave is nothing but the sum of the two original waves.

This is a phenomenon (or better, a property of several phenomena) called linearity. When specifically discussing about waves one refers to the Superposition Principle, which is the basis of stuff like constructive/destructive interference:


Since sound waves are usually not boring sine waves, these illustrations should just give an idea

[edit: meaning that it's very unlikely to have such simplified A+B = 2A and A+B = 0 cases with two different complex soundwaves...]

2 ] ...but please always remember that sound is waves moving in a three-dimensional space, so to visualize a bit better what's happening take this nice drawing here


and add one further dimension: imagine spheres instead of circles. So yes, two sounds merge, but they do so differently in different points of space - which is, amongst the other things, why you are able to distinguish which instrument is playing on your left and which on your right, as the way in which the waves will sum at your left and right ear will be different..

3 ] ..and furthermore, all this is definitely nice, although in real-real-world linearity is an extremely rare property, and only holds for certain cases. Luckily, when talking about sound, "most" of what happens is very well described in terms of linearity, but just as food for thought one should mention that there are subtle, minimal differences between reality and the physical model.

Other answers added extra phenomena to the game, but I think that goes beyond the question. Speaking about the sound waves generated by two (or, well, more) instruments, this should pretty much sum it!

edit: I see now that you also asked about what happens if sounds are not generated at the same time. Well, it doesn't really matter so much, the principle is the same. If the two fishermen in the above picture had cast their baits at different times, then the earlier one would have created waves that would have travelled farther (a bigger outside circle) and met the other waves in differenet points. The underlying principle remains the same!


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Sort of, although the meaning of this can be debated by philosophers for hours.

In a space, sound waves emanating from any point will be effectively added up in any point, in particular the point you place your ear or microphone in. However, because of the propagation delay, a small phase difference generally appears even when moving the ear or microphone a relatively small amount of space, and if you should happen to have multiple ears or microphones, you will end up receiving multiple signals which each represent the sum of all the individual instruments audible in their locations, and the signals will generally not be equal. Besides propagation delay, there's also attenuation and reflection, and if the ear or microphone happens to be big and include multiple sensor elements for different frequency ranges — as mammals' ears usually do —, a philosopher may ask if the signal recorded by such an ear is to be considered a single signal or a sum of multiple sub-signals.

Acoustics is complicated. Fourier theorem is but its cute introduction.

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  • A good point. As others say, summing two one-channel signals of different instrument does give a one-channel signal that sounds like two different instruments, but a live performance isn't exactly similar to listening to mono audio. – JiK Apr 3 '18 at 10:08
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    Philosophers don't know [redacted] about reality. There's perfectly solid science behind signal propagation and neurological interpretation thereof. – Carl Witthoft Apr 3 '18 at 13:17
  • It's a shitty philosopher who can't debate over what he or she doesn't know. In this context, due to the context uncertainty problem, some philosophers who are good at not knowing what they are talking about actually have good points. For example, asking whether it's still a single sound if you can set up multiple microphones and get different recordings came in very handy in the process of inventing stereophonic recording. There are some similarly good contexts for modelling sound using tensors rather than a small number of waveforms. But in many other contexts, it would be overkill. – dig Apr 3 '18 at 15:09
  • Having sounds come from multiple sources can also add realism to the environment. "Surround sound" systems do that with a Subwoofer to produce low bass sounds, a center front speaker for central language (for movies for example, or for the center of the orchestra), and then left/right front speakers and left/right rear speakers for offscreen noises, or additional music hall ambience. Then sounds can be created that can seem to come from all directions around you, taking advantage of your 2 ears and the brain's processing of time difference of sounds to create distance. – CrossRoads Apr 3 '18 at 15:33

All of the other answers here tell you pretty much everything you need to know if you want to record a performance. But there's a difference between listening to a recording and actually being there.

Sounds coming from different instruments in the ensemble (and even from different parts of the same instrument) follow many paths as they reflect of walls, floor, ceiling, and everything else in the room on their way to your ear. Part of the "liveness" of a live performance has to do with how sounds following different paths re-combine at any particular point in space (e.g., at the diaphragm of a microphone, or at the diaphragm of your ear.) That's part of the picture, but there's another part.

Microphones on stands generally do not move and turn while the musicians play. Your head does. The other aspect of "liveness" is how the sound changes in response to you shifting in your chair, nodding, or turning your head. I'm pretty far from being an expert in the physiology of sound perception, but I believe that the correlation between how you move, and how the sound of things changes when you move plays a role in how your brain turns sound into a sense of the space that encloses it.

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