What is the mathematical representation of pressure and amplitude in a 1D wave?

[chrom68]

Given a wave that begins at a point source that travels outward spherically, i know that for a 1D wave (from the solution of the wave equation) the amplitude at a given radius and time from the point source is:

1) A(r,t) = (1/r)*A(0)*sin(kr-wt) (or is this cosine because we take the real part of the full solution which is of the form e^i*theta = cos(theta) + i sin(theta)??). Many sites on the net use the sine form.

2) I wanted to know what the pressure at a particular radius and time was.
I know it resembles the equation for A(r,t) because they are proportional. Again is it a sine or cosine form of solution?

3) Even though this is a traveling wave, does the wavelength (between peak amplitudes/pressures for example) remain the same as it travels??

 

[Meir Achuz]

1) Whether it is sine or cosine is unimportant. Either is fine. It just depends on how the wave started long ago.
2) The wave is a pressure wave, so A should already represent the pressure.
It is the pressure in a sound wave that affects your ear.
The amplitude of movement is 90 degrees out of phase with the pressure, so if one is sine, the other would be cosine.
3) The wavelength and frequency remain the same as n your equation.