Acoustic point source

An acoustic point source idealizes a compact emitter as a localized source of sound. The approximation is useful when its size is small relative to the relevant wavelength and observation distances; the actual emitter can be a vibrating object or a small driven volume of gas.

An isotropic outgoing wave in an unbounded lossless three-dimensional medium has pressure amplitude proportional to $1/r$ and sound intensity proportional to $1/r^2$ in the far field. Multiplying that intensity by a sphere's area gives a constant radiated power. The singular behavior at $r=0$ belongs to the idealization: the source's finite geometry and near field must replace it there.