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I'm sure this is a monumentally stupid question buy I'm just stumped. I'm not sure how sound frequency is different than beats per sec from a physics perspective. Humans can hear down to 20HZ which is 20 compression waves per second isnt it? But when I tap something at 20 beats per second I'm also creating 20 compression waves per second. Clearly I can hear 20 beats per second and it only becomes more distinguishable as I go lower, so I'm clearly wrong on my interpretation, I'm just not sure how. I know I could tap a 440 Hz tuning fork, allow it to ring for 500ms, do that 20 times per second, and I'd have 20 cycles per sec samples of a 440 cycles per second sound, but if they're both compression waves, what's going on?

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  • $\begingroup$ Re, "I'm not sure how sound frequency is different than beats per sec from a physics perspective." Why do you think it is different? The Earth's atmosphere is capable of transmitting so-called "infrasound" signals, where the frequency is expressed in seconds per cycle instead of the other way around, over distances of many miles. Just because your ears are not equipped to perceive infrasound does not mean that the physical principles that underlie it are any different from the physical principles that underlie the sounds that you are able to hear. $\endgroup$ – Solomon Slow Aug 2 '19 at 13:01
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    $\begingroup$ P.S., Any periodic signal can be mathematically decomposed into a sum of sinusoids of different frequencies. Your ears are equipped to actually do that--they contain thousands tiny receptors, each of which resonates with a different frequency. If a sound continuously stimulates some combination of those receptors, then you perceive it as a continuous combination of tones. If the sound contains frequencies lower than any that your ears are equipped to perceive as distinct tones, then you perceive that as the sound changing over time. $\endgroup$ – Solomon Slow Aug 2 '19 at 13:09
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You are exactly right in your thinking. The reason you are confused is that you know humans can't hear below 20Hz but if you are tapping something at 5hz you can definitely hear it. How is this possible? It's because when you tap an object (say the desk with your fingernail) you are creating many frequencies at once. You could download a fft waterfall app for your phone and test this for yourself. The reason it contains many frequencies is that the sound wave resembles an impulse function (a sharp spike). When people say humans can't hear below 20hz they mean that they can't hear a pure sine wave below 20hz.

If you have a good subwoofer you could have it output a 10hz sine wave that you couldn't hear, but you could feel. In real life you can actually hear the 10hz from a subwoofer if it is loud enough because other things in the car will start to vibrate and emit sounds at higher frequencies. But if the subwoofer is made well it will not distort the 10hz sine wave (by rattling or emitting sound at other frequencies) and will therefore be silent. You can also make a 10hz sound by tapping on something, but it will have a ton of other frequency content higher than 10hz that makes it possible to easily hear.

Beats per second and frequency are exactly the same thing. If you tap a 440hz tuning fork 20 times per second you will get a mixture of 20hz and 440hz sound coming from it. The reason for this lies in the mathematics of the fourier transforms. This math tells us that any arbitrary waveform (like the impulse from tapping your desk) can be broken down into a sum of sine waves (like your tuning fork).

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  • $\begingroup$ Thanks, I think i get it and what remains of my confusion lies in how the brain processes sound. Off to study that now. Thanks. $\endgroup$ – M D Aug 2 '19 at 19:24

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