Abstract
The sound field of a circular piston in an infinite rigid plane baffle is calculated when the motion of the piston consists of the conventional uniform velocity normal to the plane of the piston plus a wobbling motion about a diameter of the circle: as an axis. There is a net resultant moment owing to the wobble; this moment is proportional to an integral of the square of the farfield pattern function over real and imaginary angles. A wobble impedance is defined as the moment divided by the angular velocity of the wobble. The real part of the wobble impedance is obtained from the integral of the square of the farfield pressure over real angles, and the imaginary part is obtained from the real part by the use of the Kramers-Kronig, or dispersion relations. Numerical results for the wobble impedance are presented. It is shown that for small pistons a merely wobbling piston is less efficient as a generator of sound than the customary uniform-velocity piston.
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