Suppose the human auditory system could perceive sound waves of 1 Hz. Also suppose that a single source generated waves of such frequency. Would these waves sound as though they beat? I ask because it seems to me that if two waves can interfere to produce a wave of the same form as that generated by a single source then both waves should sound the same.
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A single source generating a 1 Hz wave cannot beat.
Beating occurs because of the interference of two waves at very similar frequencies.
For example, if you have a 46 Hz and a 40 Hz wave, they would produce an audible beat with frequency $$f_{beat} = f_1 - f_2 = 6 Hz$$
You say:
it seems to me that if two waves can interfere to produce a wave of the same form as that generated by a single source then both waves should sound the same.
I've set up the following image so that you can see what happens to the amplitude of wave 1 (red), wave 2 (blue) and their superimposition (green) over the course of one second. I hope it's apparent that the envelope of the waveform has six oscillations. That's the $6 \ Hz$ tone that is audible.
A constant single-frequency source by itself has no way of producing this type of envelope.
answered Feb 17, 2018 at 1:25