# Superposition of sound waves

#### broegger

how are we able to clearly distinguish two different sound waves - like when someone is talking to us while music is playing in the background... i've read it is due to the superposition principle which states that the waves combine and form a resultant wave that is the sum of the individual waves..

I don't quite understand how this implies that we can distinguish which individual waves a resultant wave is made up of.. how is the brain able to determine these individual waves from the resultant wave - isn't there an infinite number of possible waves that can combine and form a given resultant wave??

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#### krab

broegger said:
..

I don't quite understand how this implies that we can distinguish which individual waves a resultant wave is made up of..
Well, you are right. Superposition rather implies we would not be able to tell. There are 2 ways the human can separate sounds. One is that there are 2 ears. This allows one to determine sound direction, allowing the brain to ignore sounds coming from the wrong direction. The other is visual. You watch a person speaking and can use this with the sound input to disentangle the sound signal from the ears. I have a friend who is blind and he has a really hard time in conversation when the room is filled with other conversations as well.

#### Integral

Staff Emeritus
Gold Member
In mathematics this phenomena is know as Fourier Analysis. It is possible to break down any waveform into a sum of individual sine waves with different frequencies of varying amplitudes. This representation is unique. This means if you change the one of component waves you change the result. Fortunately small variations from a given waveform sound about the same, thus the modern recording industry exists.

The more you learn and understand of this branch of mathematics the more appreciation you gain for the functionality of ears and the brains ability to sort out this information.

#### broegger

thanks for answering, but I still don't understand how we are able to sort out the individual wave-components in a composite wave..

i'm not really sure if I understand integral's comment, but what I get from it is that there is only one possible combination of individual wave components that could have caused the perceived resultant wave and this is how we are able to seperate sounds.. is this really true??

#### Doc Al

Mentor
Fourier's Theorem

broegger said:
i'm not really sure if I understand integral's comment, but what I get from it is that there is only one possible combination of individual wave components that could have caused the perceived resultant wave and this is how we are able to seperate sounds.. is this really true??
Yes, any periodic wave can be decomposed into a unique set of "pure" sine/cosine waves. This is Fourier's theorem.

#### krab

Doc Al said:
Yes, any periodic wave can be decomposed into a unique set of "pure" sine/cosine waves. This is Fourier's theorem.
And further, the sounds are detected in the spiral-shaped cochlea in the human ear. If the cochlea is imagined to be unrolled, it tapers to a point. Sounds of given wavelength only travel as far as they "fit". There are sensors all along it, so it acts like a spectrum analyzer.

#### turin

Homework Helper
The cillia in the choclea are also at resonant lengths, so I've heard.

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