# The properties of sound?

1. Aug 9, 2011

### onnyctip

Greeting Physics Forums; my first post here. Thanks in advance for your time!

Approximately how many soundwaves compose what we can say is a single noise, like a drumbeat?

I know there are multiple frequencies involved and our brain interprets this in it's own way. There is interference and phasing and I read that the Fourier method(?) helps with this.

Simply can you derive a single soundwave from let's say a car crash, or is it a high-order more of soundwaves like each square inch of metal on metal collision producing multiple waves and our brain (or a recording device) forming a general picture?

2. Aug 9, 2011

### Pythagorean

welcome to PF, onny.

drum beats are composed of a wide range of audible frequencies, so they fill up the audio spectrum pretty well; on the other hand, they generally don't resonate as long so you have a lot of soundwaves all at once (as opposed to a note played on a string: relatively few frequencies that resonate for a long time).

http://nylander.wordpress.com/2003/11/10/mode-of-vibration-of-a-circular-membrane/

You have bones in your ear that convert the frequencies to motion in a fluid filled chamber by vibrating a membrane that makes up a wall of the chamber. Hair cells hang out of sensory neurons and as they sway in the fluid, coding the frequency of the swaying for downstream neurons to interpret. There is a lot of processing that goes on in the audio and parietal cortices after that before it reaches your hippocampus and/or prefontal cortex (when it's integrated with the rest of your experience into a whole picture). We still don't have a clear picture of that mess (though we do have collage of several pictures ).

We interpret a double in frequency (an octave). As the "same note, only higher". So a Middle C oscillates at twice the frequency as the C below it does (and of course, half the rate of the C above it).

Fourier assumes everything is comprised of sins and cosines, but that's not quit the truth. If you Fourier decompose the action potential of a single neuron with a short-time fourier transform, you get noise that's more dense during the spike, it's not especially informative. However, whole populations of neurons have a more rhythmic, sinusoidal shape (i.e. brainwaves).

You can't uniquely decompose the whole signal you hear, but you can make reasonable approximations if you know the "ground truth" or some of the physics about what actually happened at the source.

You can improve your accuracy by having more sampling sites. 5000 ears spread around the intersection, all connected to one brain might be able to reconstruct the accident a lot better, because you'll be able to easier resolve the spatial location of each wave. Remember the waves are spherical, so they create a three dimensional acoustic picture that will be much "more unique" than your two ears can interpret.

3. Aug 10, 2011

### onnyctip

What a great response! Thank you!

4. Aug 10, 2011

### KingNothing

+1 for Pythagorean!