Acoustic wave radiation

Most acoustic waves are induced by the vibration of mechanical surfaces. The interactions between a vibrating body and the propagation medium obey highly complex laws based on the existence of two forms of energy:

• propagated energy that moves away from the source as long as the wave encounters no obstacle or change in impedance;

• energy exchanged between the source and the propagation medium.

The first form of energy corresponds to the real part of the radiation impedance; the second corresponds to the imaginary part.

Radiation impedance is therefore the quantity that best characterizes the quantities of energy involved. Its expression can be easily established in a few simple cases, giving rise to widely-used models.

In addition to radiation impedance, these models are characterized by their own radiation energy distribution laws. These laws are translated into graphical representations called directivity diagrams.

These two parameters can be used to classify elemental source models into two groups: omnidirectional and directional.

• Omnidirectional models

These are mainly :

• the pulsating sphere, which translates quite correctly the radiation from omnidirectional sources;

• the source point or monopole, a special case of a pulsating sphere.

• Directional models

These models can be grouped into two categories:

• combined directivity models obtained by combining several monopoles: dipoles, embedded monopoles, quadripoles, linear arrays, etc. These combinations constitute sources whose directivity is of interference origin. These associations constitute sources whose directivity is of interferential origin;

• models with intrinsic directivity, the most representative of which is the embedded circular planar piston. This model, obtained from the study of monopole distributions, is an archetype for describing the behavior of a large number of sources with a flat vibrating surface (room wall, airplane wing, vibrating table, etc.) or inducing an approximately flat wavefront (opening in a wall, end of a pipe, loudspeaker, etc.).

This is the model best suited to describing speaker radiation.

Acoustic wave propagation has been studied in detail in article [TE 5 130] of this treatise. References to general works [1] to [11] can also be consulted....