ABSTRACT
In Chapter 2 it was shown that Hij was the transfer function that gave the output at j per unit sinusoidal input at i. Suppose there is an acoustic ˜eld generated by a group of sound sources and that these sources are surrounded by an imaginary surface So, as shown in Figure 10.1. Through each element of So sound passes into the ˜eld. Thus, each element of So, denoted by ds, can be considered a source that radiates sound into the ˜eld. Consider the pressure dp(P,ω) at ˜eld point P at frequency ω due to radiation out of element ds:
dp P H P S p S dsp( , ) ( , , ) ( , )ω ω ω= (10.1)
where Hp(P, S, ω) is the pressure at ˜eld point P per unit area of S due to a unit sinusoidal input pressure on S. The total pressure in the ˜eld at point P is
p P H P S p S dsp
S ( , ) ( , , ) ( , )ω ω ω= ∫
(10.2)
If motion (e.g., acceleration) of the surface S is considered instead of pressure, the counterpart to Equation 10.2 is
p P H P S a S dsa
S ( , ) ( , , ) ( , )ω ω ω= ∫
(10.3)
where H(P, S, ω) is the transfer function associated with acceleration; that is, it is the pressure at ˜eld point P per unit area of S due to a unit sinusoidal input acceleration of S.
