Sound is propagated by waves. Waves can interfere.
Suppose there are two tenors standing next to each other and each singing a continuous middle-C.
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Will it be the case that some people in the audience cannot hear them because of interference?
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Would it make a difference if they were two sopranos or two basses and singing a number of octaves higher or lower?
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How does this generalize to an array of n singers?
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Given a whole choir, to what extent are their voices less than simply additive because of this? Is it possible that, for some unfortunate member of the audience, the choir appears to be completely silent–if only for a moment?
Best Answer
The main issue in the setting of an orchestra or choir is the fact that no two voice or instruments maintain exactly the same pitch for any length of time. If you have two pure sine wave source that differ by just one Hertz, then the interference pattern between them will shift over time - in fact at any given point you will hear a cycle of constructive and destructive interference which we recognize as beats, but the exact time when each member of the audience will hear the greatest or least intensity will vary with their position.
Next let's look at the angular distribution of signal. If two tenors are singing a D3 of 147 Hz (near the bottom of their range) the wavelength of the sound is 2 m: if they stand closer together than 1 m there will be no opportunity to create a 180 degree phase shift anywhere. If they sing near the top of their range, the pitch is closer to 600 Hz and the wavelength 0.5 m. But whatever interference pattern they generate, a tiny shift in frequency would be sufficient to move the pattern - so no stationary observer would experience a "silent" interference - even of the fundamental frequency.
Enter vibrato: most singers and instruments deliberately modulate their frequency slightly - this makes the note sound more appealing and allows them to make micro corrections to the pitch. It also makes the voice stand out more against a background of instruments and tends to allow it to project better (louder for less effort on the part of the singer). This is used by soloists but more rarely by good choirs - because in the choir you want to blend voices, not have them stand out.
At any rate, the general concept here is incoherence: the different source of sound in a choir or orchestra are incoherent, meaning that they do not maintain a fixed phase relationship over time. And this means they do not produce a stationary interference pattern.
A side effect of interference is seen in the volume of a choir: if you add the amplitudes of two sound sources that are perfectly in phase, your amplitude doubles and the energy / intensity quadruples. A 32 man choir would be over 1000 times louder than a solo voice - and this would be achieved in part because the voices could only be heard "right in front" of the choir (perfectly coherent voices would act like a phased array). But since the voice are incoherent, there is no focusing, no amplification, and they can be heard everywhere.
Note that incoherence is a function of phase and frequency - every note is a mix of frequencies, and although a steady note will in principle contain just a fundamental and its harmonics, their exact relationship is very complicated. Even if you took a single singer's voice, and put it into two speakers with a delay line feeding one of the speakers, I believe you would still not find interference because of the fluctuations in pitch over even a short time. Instead, your ear would perceive this as two people singing.
And finally - because a voice (or an instrument) is such a complex mix of frequencies, there is in general no geometric arrangement of sources and receiver in which all frequencies would interfere destructively at the same time. And the ear is such a complex instrument that it will actually "synthesize" missing components in a perceived note - leading to the strange phenomenon where for certain instruments, the perceived pitch corresponds to a frequency that is not present - as is the case with a bell, for example.