# HW8 - ECE 473/TAM 413 Homework Assignment #8 Due: Friday,...

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ECE 473/TAM 413 Homework Assignment #8 Due: Friday, October 31, 2008 1. For the plane piston, circular source of radius a, we derived the pressure for both the Fresnel Zone (on-axis only) and the Fraunhofer Zone, that is, p r,t ( ) = 2j ! o cU o e j " t e # j k 2 R 1 + r ( ) Sin k 2 R 1 # r ( ) \$ % ( ) p r, ! ,t ( ) = j "# o a 2 U o 2r e j " t \$ kr ( ) 2J 1 kaSin ! ( ) kaSin ! % ( ) * . Show that in the far field, both of these expressions reduce to the same on-axis expression. 2. A hemisphere of radius “a” and a circular piston of radius “a” are each mounted so that they radiate on one side of an infinite baffle. They are both vibrating with the same maximum speed amplitude U o and at the same frequency so that ka << 1. (a) For a distance such that r >> a, determine the ratio of the axial intensity of the piston to that of the hemisphere. (b) Determine the ratio of the total power radiated by the piston to that radiated by the hemisphere. 3. A rectangular flat piston vibrator with sides at y = ±a and z = ±b vibrates at a radian frequency

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## This note was uploaded on 09/19/2009 for the course ECE 473 taught by Professor Obrian during the Fall '08 term at University of Illinois at Urbana–Champaign.

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HW8 - ECE 473/TAM 413 Homework Assignment #8 Due: Friday,...

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