Structural Acoustics

34 Structural Acoustics: Deterministic and Random Phenomena

© 2011 by Taylor and Francis Group, LLC

2.8 Sound Radiation and Vibration

2.8.1  Helmholtz Integral, Sommerfeld Radiation, and Green’s Function

In this section, acoustic elds that satisfy the wave equation of linear acous-

tics are of interest:

c p p t

2 2 2 2

∇ = ∂ ∂/

(2.72)

where p is the pressure in the eld at point P and at time t. For sinusoidal

time-varying elds,

p P t p P e

i t

( , ) ( )=

ω

(2.73)

so that p satises the Helmholtz equation:

∇ + = =

2 2 2 2 2

0p k p k cω /

(2.74)

This Helmholtz equation can be solved in general form by introducing

an auxiliary function called Green’ ...