Split Wave: Practical Approach to Separate Components

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Homework Statement


how do u split a resultant wave(formed by interference of many)into its constiuent waves?(practically){not light,i'm actually thinking of sound,beats}

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The Attempt at a Solution


i tried to use the Fourier series,and split it into sine and cosine waves.how do u do it practically?
 
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if its a light wave with different frequency components, a prism or diffraction grating would do the trick... or 2 mirrors a tunable distance apart to pick out frequencies
 
no sir,i'm actually thinking of sound and beats formed
 
like the one inthe fig attached.how do u split these waves experimentally?what about the ones that have no order,say like the group wave associated with an electron.i tried to use Fourier series to get periodical sine and cosine waves.but i don't know how to do it experimentally.
 

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