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Modified Acoustic Intensity Derivation

The acoustic particle velocity in the r direction, U, is in phase with the acoustic pressure, p, everywhere in the far field of a simple acoustic source radiating spherical waves. The quantities p and U are related by the characteristic impedance as

equation20

using the notations of Ref. 1 wherein a far field assumption was assumed but not stated.

In general p and U are related by the r component of Euler's equation, tex2html_wrap_inline125 = 0 [2],[3]. Suppose that in the near field of a time harmonic source one has the pressure

equation23

Then the corresponding particle velocity component in the r direction is

equation26

One can see that as kr becomes very large in the far field, the simple plane wave relation Eq. (1) results. The real parts of Eqs. (2) and (3) are

equation30

and

equation32

respectively.

In Ref. 1 the additional nearfield term of tex2html_wrap_inline131 in Eq. (5) was omitted. Thus the corresponding equation for the instantaneous intensity should be

equation34

The time averaged intensity is then

equation37

which is unchanged from Ref. 1.



VICTOR W SPARROW
Fri Aug 30 16:31:47 EDT 1996