Many sounds, one speaker

Classical Mechanics Level 2

Recordings that get played speakers can be very detailed, consisting of tens or hundred of distinct sound sources, each of which contribute a continuum of frequency components. Yet there is only one speaker. How is it possible for a single speaker to faithfully reproduce complex sounds?

Speakers play the most intense sound at any given time, our brains piece it back together. The speaker plays all the frequencies, this is why speakers usually have rings. Each frequency is played for a very small amount of time, in sequence with the others. The speaker has a time-dependent position, which is set by the sum of the component soundwaves.

2 solutions

Agnishom Chattopadhyay
May 3, 2015

The principle of superposition much of the work in this situation. The sound amplitudes add up to form a resultant and it suffices to play that.

To get back the individual waves, you need to do a fourier transform.

Clean up the grammar so that the question is understandable.

Robert Gallenberger - 4 years ago

what a brain mama

Sai Phanindra - 5 years, 6 months ago

so does this mean that the speaker is capable of reproducing complex sounds due to some sort of encoding/decoding ?

Lavann D Hoggard - 5 years, 3 months ago

Isn't that the same thing what happens to our ears when we listen to such complex sound waves, speaker is behaving the same way and consequently our senses can't differentiate whether signals are from original source or the speaker...

Kamal Gurnani - 2 years, 6 months ago

Poor solutions description. And poor grammar..makes it hard to understand. Not the way to go to encourage subscription

Jason king - 2 years, 2 months ago

It's an *interference tho, not a superposition

Kolega Kierownik - 7 months ago

Max Yuen
May 3, 2019

A speaker actually cannot produce all possible frequencies. It has a band limited frequency response, which is given in "Fourier" space as $H(\omega)$ .

A piece of music which can be viewed as a sum of various instruments can be reconstructed from the various components (which can have time dependent contributions) as the following:

$f(t) = \int_{-\infty}^{\infty}{H(\omega)(A(\omega;t)\sin(\omega t)+B(\omega;t)\cos(\omega t))\frac{d\omega}{2\pi}}$ .

In reality, the Fourier transform isn't ideal to describe a complex piece of music. Normally we would do a moving window Fourier transform.

In more advanced analysis, the better way is to present these with wavelets. This is the basis of audio compression (which by the way also works for image analysis and compression.)

Many sounds, one speaker

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