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## Pressure radiation from a piston terminated in an infinite baffle

Consider a rigid piston in a rigid infinite baffle as shown in figure 3.1. The piston vibrates uniformly with a sinusoidal velocity of amplitude normal to the baffle. In order to calculate the behaviour of this system, we split the piston into infinitesimal simple source elements and sum the resulting pressure fields. A piston surface element of area is present at . This surface element oscillates with a velocity amplitude of normal to the baffle and acts as a simple source of spherical pressure waves. These are represented on the diagram by a hemispherical shell, with the acoustic pressure at a distance from the source element given by (3.2)

where is the simple source strength and a time factor is assumed throughout. The part is known as the Green's function and implies that the pressure oscillates sinusoidally in space with wavelength and with an amplitude that dies as . Integrating (3.2) over , the surface of the whole piston, we get the total pressure field due to the sum of all the source elements that make up the piston. (3.3)

Note that the integrand is singular (tends to infinity) as tends to zero. This problem must be addressed before numerical integration is possible.

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Jonathan Kemp 2003-03-24