Remarks
Acoustic wave propagation

The fundamental differences between spherical divergent waves and travelling plane waves are :

• pressure decay in 1/r ;

• the phase shift between pressure and speed.

This phase shift is due to the complex nature of the specific acoustic impedance of the spherical wave, which was real (Z_S = ρ₀c) in the case of the traveling plane wave.

The consequences of phase shifting are different for near-field and far-field applications.

• In the near field (kr << 1): cos Ψ " 0 and Z_R " jρ₀c kr.

Pressure and velocity are almost in quadrature, the medium is highly reactive (imaginary impedance) and most of the energy is exchanged between the medium and the source.

Speed decreases in 1/r ² and pressure in 1/r.

• In...