Radiation Patterns From a Vibrating Plate

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Radiation Patterns From a Vibrating Plate
Eleazer Bromberg
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S. R. D. No. 7O6 "Directivity of Soueed in Water - Elementary Arrays" C4 - MDRC - O72 R ADIATION PATTBRIJ3 FROM A VIBRATING PLATE by E, Bromberg and H, Cohn The problem of the control of the directivity pattern of sound radiated from a vibrator set in an infinite rigid wall or "baffle" has recently* been treated by the Harvard Underwater Sound Laboratory and by Dr. Harry Nyquist of Division C Section 4, Their vibrators con- sisted of line sources and point sources, ** Tfe wish to consider the s...ame problem for a two-dimensional array of sound sources so denseljr packed that it may be considered as a continuous surface distribution of a vibrating plate. Vfe assume further that the overall dimensions of the plate and the frequency of vibration have been specified.
We take our plate in the x-y plane vibrating in the '^ z- direction, so that the eqxjation of the surface of the plate at any time t is (1) z = Re ': f(x, y) e '^"^^^ where f(x, y) is a given amplitude function, extending over the projection of the plate on the x-y plane.


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