Acoustic wave propagation

Acoustic wave propagation obeys the same laws as most wave-theory phenomena. Any disturbance induced in an elastic medium gives rise to a local deformation which travels at a speed that depends solely on the physical properties of the medium in question. Theoretically, this motion is fully described by a partial differential equation, a function of space and time. In practice, this equation can be reduced to a time-independent propagation equation. It is then called the Helmholtz equation. The solution to this equation enables us to study all propagative phenomena, and in particular :

• progressive plane wave motion, whose main characteristic is the nullity of the phase between pressure and velocity;

• stationary plane wave motion, which occurs as soon as the travelling plane wave encounters an obstacle or a change in the impedance of the propagation medium. This type of propagation is characterized by a complex phase relationship between pressure and velocity. This relationship can be precisely described by the expression of the impedance ;

• the movement of progressive spherical waves, whose main characteristic is the difference in behaviour between the near field (pressure and velocity almost in quadrature) and the far field (pressure and velocity in phase);

• the motion of standing spherical waves induced by the presence of obstacles of the same shape as the wave fronts.

Most commonly used acoustic problems can be tackled using two elementary models:

• the quasi-stationary plane-wave model, which can be described by calculating the impedance and applies to all acoustic phenomena occurring in waveguides. In the special case where the wavelength is long compared with the dimensions of the waveguides (low-frequency approximation), the model can be used to determine all the acoustic circuit constants, enabling a simplified representation known as the "equivalent diagram";

• the spherical traveling wave model, which predicts the behavior of all waves emanating from omnidirectional sources placed in a free field.

This article deals with the propagation of acoustic waves. To understand acoustic wave radiation, please refer to the following article of this treaty.

For a detailed study of the general laws of acoustics, please refer to references [1] to [12].