I'm trying to understand how a vibrating body produces oscillations in sound pressure. I've been through derivations and solutions of the wave equation for a string, but I don't understand the transition from waves on a string to sound pressure waves. How are the waves on a string or drum membrane mathematically related to the sound waves they are supposed to create? Suppose ##y(x,t)## is the displacement of a string from equilibrium position. Does perhaps ##y=d## where ##d## is the average particle displacement from equilibrium position? Also, I've been through Feymann's derivation of the wave equation where he assumes the wave fronts are planar, and only uses one spacial dimension. This seems extremely idealistic to me. As I understand it, waves radiate out spherically from a point source. Are the dimensions of the eardrum and typical distances from a sound source such that the segment of the spherical wave fronts that comes into contact with it are able to be considered planar?