HW7_solution473 - ECE 473/TAM 413 Homework Assignment #7...

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Homework Assignment #7 Solutions - 1 ECE 473/TAM 413 Homework Assignment #7 Solutions 1. A pulsating sphere of radius a = 0.15 m radiates spherical waves into air at a frequency of 100 Hz. (a) The intensity at a distance of 0.5 m from the center of the spherical source is 10 W/m 2 . Determine the total acoustic power passing through the surface of a sphere of radius 0.5 m centered on the spherical source. (b) At the surface of the sphere, r = a, compute the intensity and the amplitudes of the acoustic pressure and particle velocity. a) ! = 4 " r 2 I = 4 " 0.5 m ( ) 2 10 W/m 2 ( ) = 31.4 W b) I r = 0.15 m ( ) = I r = 0.5 m ( ) 0.5 /0.15 ( ) 2 = 111W/m 2 p o = 2 ! o cI = 2 415 rayl ( ) 111W / m 2 ( ) = 304 Pa u o = p o ! o cCos " ( ) = 304 Pa 425 rayl ( ) Cos 74.64 o ( ) = 2.77 m /s where ! = Cot " 1 ka ( ) = Cot " 1 0.2748 ( ) = 74.64 o 2. Consider a simple monopole source radiating into free space (something like a loudspeaker high above a football stadium rather than in a living room). In order to produce sound of frequency 1000 Hz and level SPL = 100 dB at a distance of 15 m, (a) what must be the source strength Q (rms), (b) what must be the intensity and (c) what must be the total acoustic power radiated? Assume it is a nice sunny day at 20˚C. In air at 20˚C, ! o = 1.21kg / m 3 , c = 343 m / s , and z = 415 MKS rayl a) SPL = 100 dB = 20 ! log 10 p o p ref " # $ % & p o r = 15 m ( ) = p ref ! 10 5 = 20 μ Pa ! 10 5 = 2 Pa (rms) 2.828 Pa(peak) " # $ p o = ! o ck 4 " r Q Q o (rms) = 4 ! rp o (rms) " o ck = 4 ! rp o (rms) " o # = 4 ! 15 m ( ) 2 Pa ( ) 1.21kg / m 3 ( ) 2 ! $ 1000 / s ( ) = 0.0496 m 3 / s b) I = 1 8 ! o c Q o " r # $ % & ( 2 = 415 Pa ) s/ m 8 0.0496 m 3 / s 2 0.343m ( ) 15m ( ) # $ % & ( 2 = 9.63mW / m 2 c) ! = 4 " r 2 I 15m ( ) = 4 " ( ) 2 9.63 mW/ m 2 ( ) = 27.3W 3. A 0.2-m-radius hemispherical sound source is mounted near to a rigid plane boundary and radiates harmonic diverging spherical waves into sea water (13˚C) at a frequency of 500 Hz. If the SPL at a distance of 4 m from the source is 50 dB (re: 2 μbars peak), then determine the peak surface displacement amplitude of the source.
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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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HW7_solution473 - ECE 473/TAM 413 Homework Assignment #7...

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