Re: What is the equasion for a sound wave?

Sound waves are generated by something moving back and forth in air and can 
be called a vibrating body.  The back-and-forth motion of the vibrating 
body can have many different forms but can be visualized as a graph.  The 
graph of the back and forth motion as a function of time is called a 
waveform.  Waveforms can be very complex.

The simplest repetitive back- and-forth motion is called simple harmonic 
motion.  This is the kind of motion characteristic of a loudspeaker 
diaphragm when it is producing a pure tone.  The back and forth motion can 
be graphed, in this case by plotting the displacement of the loudspeaker 
diaphragm as a function of time.  At rest, the position of the diaphragm is 
at zero displacement.  The displacements when it is producing sound go back 
and forth around this zero point.

A back-and-forth motion can also be depicted as a line rotating around a 
point, much like the hand of a clock moving in a clockwise direction.  Noon 
represents the zero point of the loudspeaker diaphragm movement, 3 o'clock 
represents the maximum excursion of the loudspeaker diaphragm in one 
direction, 6 o'clock again represents the zero point of excursion, 9 
o'clock represents the point of maximum excursion but in the opposite 
direction, and finally, noon represents the completion of one back and 
forth motion back to the zero starting point.  This rotation of a line 
could be described in terms of the degrees of a circle, from 0 to 360 
degrees.  The curve obtained by graphing the trigonometric sines of angles 
from 0 to 360 degrees is identical to the curve defining simple harmonic 
motion.  The resulting function is then a mathematical formula for a sine 
function.

Here is how to make a graph of a pure tone.  Make the x axis go from 0 to 
360 degrees in 10 degree increments.  Make the y axis go from –1 through 
zero to +1.  Compute the sine of zero degrees (if you are using a 
calculator make sure the sine function expects degrees instead of radians) 
and plot the result, in this case, 0.  Then do the same for 10 degrees (you 
should get 0.1736481777), then 20 degrees (you should get 0.3420201433), 
etc.  The resulting function will then be a sine function and will 
represent simple harmonic motion, or the waveform of a pure tone.

Incidentally, all other sounds, even the speech sounds you make when saying 
"Lets go to the baseball game", are simply the combinations of various sine 
waves.  Another way of looking at this is that the complex waveform of any 
sound can be broken down into its component sine waves.