# Humans don't hear below ~20 Hz, so why can we hear a singular sound?

if you clap once, you can hear a sound. This seems like a single pulse of pressure variation. Why is it audible?

Is the sound perhaps somehow a brief packet of many superimposed waves, rather than a single pulse? If you somehow generated one single pulse of sound, could a human hear it?

Could ultrasonic noise at a large amplitude damage a person's hearing?

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Dale
Mentor
If a signal has a brief duration (like a clap) then it necessarily must have a broad range of frequencies, not just a single frequency. Some of those components will be below the audible range, but most of it will be well within the audible range (20 Hz - 20 kHz).

DaveC426913
Gold Member
Is the sound perhaps somehow a brief packet of many superimposed waves, rather than a single pulse?
Yes.

Try an experiment. Surely you have a primitive sound recorder on your computer? Don't they all come with one nowadays? You can always download 'Audacity'.

Record a clap. Look at the waveform. You'll be able to see exactly what it looks like at any level of detail you choose.

If you somehow generated one single pulse of sound, could a human hear it?
No, but they might feel the pressure wave. A bomb does this. Though don't confuse the pressure wave with the reverbs that follow.

Could ultrasonic noise at a large amplitude damage a person's hearing?
Certainly.

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that would also go for sounds under 20 hz right

DaveC426913
Gold Member
that would also go for sounds under 20 hz right
What would?

Recording it? Feeling a pressure wave? Damage?

Well, yes.

rbj
if you clap once, you can hear a sound. This seems like a single pulse of pressure variation. Why is it audible?
because it contains all sorts frequency components that are in the audible range.

Is the sound perhaps somehow a brief packet of many superimposed waves, rather than a single pulse?
if you believe Joe Fourier, sure!

If you somehow generated one single pulse of sound, could a human hear it?
depends on how high and how wide the pulse is.

Could ultrasonic noise at a large amplitude damage a person's hearing?
sure, and even more, if the SPL is high enough.

some futuristic form of capital punishment might be the Lethal Sound Chamber (instead of lethal gas). strap the condemned into a sound-proof chamber and expose the poor S.O.B. to 400 dB ultrasonic SPL. that'll do more than damage his hearing.

rbj, I'd presumed futuristic societies do not employ capital punishment (are you American?)..

Zorodius, aside from Fourier decompositions, perhaps what you should research further is the biomechanics of your ear (cochlea especially).

DaveC426913
Gold Member
some futuristic form of capital punishment might be the Lethal Sound Chamber (instead of lethal gas). strap the condemned into a sound-proof chamber and expose the poor S.O.B. to 400 dB ultrasonic SPL. that'll do more than damage his hearing.
Actually, above about 250dB much of the rest of the energy just turns into heat.

DaveC426913
Gold Member
sure, and even more, if the SPL is high enough.
I'm not so sure. A truly single pulse will hit the victim, but won't register as a sound (unless there's interference causing harmonics). I mean, what frequency would it be?

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Dale
Mentor
I mean, what frequency would it be?
All of them (approximately). Fourier transform of a delta function is a constant. Equal energy at all frequencies.

DaveC426913
Gold Member
All of them (approximately). Fourier transform of a delta function is a constant. Equal energy at all frequencies.
No, I mean what freq would you hear?

Dale
Mentor
No, I mean what freq would you hear?
All frequencies between about 20Hz and 20kHz. That is, all of the audible frequencies.

DaveC426913
Gold Member
All frequencies between about 20Hz and 20kHz. That is, all of the audible frequencies.
You're saying that a single pulse would be heard as white noise - i.e. hissing.

You're saying that a single pulse would be heard as white noise - i.e. hissing.
See, this is the problem with basing too much on Fourier decomposition. Yes, mathematically there is equality between an infinitely sharp sound pulse (with silence forever before and after) and a continuous spectrum of pure notes playing (for all eternity, timed from the beginning to meet exactly in phase at that one moment). Neither basis represents exactly what human hearing is sensitive to (imagine if you could listen to each of those separate notes before you had even decided to make the clap, and couldn't even distinguish the clap-moment since you're oblivious to phase); that question is better answered by modelling hearing with a driven set of harmonic oscillators (with a finite range of different natural frequencies): you hear a "crack" when a wide range of those oscillators are just momentarily excited.

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DaveC426913
Gold Member
See, this is the problem with basing too much on Fourier decomposition.
This was my reaction too, though I'm not versed in this science.

"Fourier transform of a delta function is a constant." sounds great, but doesn't sound like it has a lot of applicability to reality.

Dale
Mentor
You're saying that a single pulse would be heard as white noise - i.e. hissing.
No, the Fourier transform of a delta function is not the same as the Fourier transform of Gaussian white noise. The Fourier transform of a delta function is a constant in both magnitude and phase. The Fourier transform of Gaussian white noise is also Gaussian white noise. In other words, if you take noise in one domain you get noise in the other domain. Noise is not constant (neither amplitude nor phase).

When noise is white it is uncorrelated, meaning that the value of the noise in one sample is not a function of the value of the noise in any other sample. Because of this, if you repeatedly sample Gaussian white noise you will have the same AVERAGE value at all frequencies. This is not the same as having a constant value at all frequencies. A constant has no spread in values at different frequencies, while Gaussian white noise would have a spread about the mean described by the standard deviation of the noise distribution (normal distribution).

See, this is the problem with basing too much on Fourier decomposition. Yes, mathematically there is equality between an infinitely sharp sound pulse (with silence forever before and after) and a continuous spectrum of pure notes playing (for all eternity, timed from the beginning to meet exactly in phase at that one moment). Neither basis represents exactly what human hearing is sensitive to
I agree completely with that. The Fourier transform and its basis functions are not exactly what we are sensitive to. Our auditory system is much more complicated and much messier. However, it is a very good first-order approximation in most cases and it has a lot of value in understanding basic questions like this thread.

(imagine if you could listen to each of those separate notes before you had even decided to make the clap, and couldn't even distinguish the clap-moment since you're oblivious to phase); that question is better answered by modelling hearing with a driven set of harmonic oscillators (with a finite range of different natural frequencies): you hear a "crack" when a wide range of those oscillators are just momentarily excited.
The wide range of frequencies obtained through Fourier decomposition is a good approximation to your wide range of oscillators. It is not exact, but conveys the basic idea in much clearer terms that more people are familiar with.

This was my reaction too, though I'm not versed in this science.

"Fourier transform of a delta function is a constant." sounds great, but doesn't sound like it has a lot of applicability to reality.
Certainly there is no such thing as a perfect delta function in reality, but I was trying to present the concept clearly and succintly. The basic point is that the shorter the duration of any pulse the broader it's bandwidth. So a clap or a brief sound pulse will not just have a single frequency, but will have a broad range of frequency components. It is actually not too difficult to make a pulse that would cover the whole audio range, it would only have to be less than about 25 us duration. It would be perfectly reasonable to approximate any sound pulse less than about 25 us or so as a delta function for most purposes.

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some futuristic form of capital punishment might be the Lethal Sound Chamber (instead of lethal gas). strap the condemned into a sound-proof chamber and expose the poor S.O.B. to 400 dB ultrasonic SPL. that'll do more than damage his hearing.
Actually, above about 250dB much of the rest of the energy just turns into heat.
how come over 250db does a ton of heat come out
shouldn't there be some type of proportion that happens between db and heat

or did you mean to say something like
the higher the db the more heat that comes out

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DaveC426913
Gold Member
how come over 250db does a ton of heat come out
shouldn't there be some type of proportion that happens between db and heat

or did you mean to say something like
the higher the db the more heat that comes out
The second one. I don't really know the curve, I just read that its not like the loudness scale just keeps going up.

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That seems sensible, since sound is actually a movement of atoms, that there should be volume beyond which the material no longer behaves elastically.