HW10_solution473 - Homework Assignment #10 Solutions - 1...

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Unformatted text preview: Homework Assignment #10 Solutions - 1 ECE 473/TAM 413 Homework Assignment #10 Solutions For your information Hour Exam 2: Wednesday, April 23, 2008, 7:00-8:30 pm Hour exams are open book (the text for the course) with one sheet of notes (you can use both sides). Your class notes and lecture notes are not permitted. You can use calculators. 1. An infinite plane wave is propagating in the positive x direction in a medium with an attenuation coefficient of 30 dB/m. Find the intensity at the distance x = 0 if the intensity at x = 4 cm is 100 W/m 2 . ! = 30 dB/m = 3.454 Np /m I x = ( ) = I x = 4 cm ( ) e 2 ! x = 100e 2 3.454 ( ) 0.04 ( ) = 132 W/m 2 2. Problem 8.2.2 in Kinsler et al. a) From appendix A10 (1 atm values), ! = 1.85 " 10 # 5 Pa # s ! = 1.21kg/ m 3 Because p = ! rT k , p ! " for constant temperature and thus at 0.1 atm, ! = 0.121kg/ m 3 . Propagation speed c is independent of p, and ! depends only on temperature. ! s = 4 3 " # c 2 = 4 3 1.85 $ 10 % 5 Pa % s (0.121kg /m 3 )(343 m /s) 2 = 1.73 $ 10 % 9 s b) f = 1 2 !" s = 92 MHz c) ! s = " c 1 2 1 + "# ( ) 2 $ 1 1 + "# ( ) 2 = 1 2 1.73 % 10 $ 9 s ( ) 343 m /s ( ) 2 $ 1 2 = 5.4 % 10 5 Np / m c p = c 2 1 + !" ( ) 2 1 + !" ( ) 2 + 1 = 2 343 m /s ( ) 2 2 + 1 = 442 m / s d) For 1 atm, ! s = 1.73 " 10 # 10 s . Therefore, ¡¢ s = 0.1 ! s = " c 1 2 1 + "# ( ) 2 $ 1 1 + "# ( ) 2 = 1 2 1.73 % 10 $ 10 s ( ) 343m / s ( ) 1.01 $ 1 1.01 = 8.4 % 10 4 Np/m c p = c 2 1 + ¡¢ ( ) 2 1 + ¡¢ ( ) 2 + 1 = 2 343 m /s ( ) 1.01 1.01 + 1 = 344 m / s 3. Problem 8.4.3 in Kinsler et al. 3....
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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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HW10_solution473 - Homework Assignment #10 Solutions - 1...

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