# HW3_solution - ECE 473/TAM 413 Homework Assignment#3...

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Homework Assignment #3 Solutions - 1 ECE 473/TAM 413 Homework Assignment #3 Solutions Note to graduate students taking the course for 4 hours of graduate credit (NB: only graduate students can receive 4 hours of credit) : For the additional 1 hour of credit, you are required to write a paper (typically about 10 pages, double spaced) that discusses in some detail any topic on acoustics for which the fundamentals of engineering acoustics are explicitly described . The paper needs to be based on 5 peer-reviewed publications. The paper will be due Monday, December 5, 2008. However, I must approve the topic and peer-reviewed publications. For the approval process, prepare a one-page outline (including 5 peer-reviewed citations) for submission Monday, October 6, 2008 . 1. Equation 5.2.1’s P = ! rT k in Kinsler et al. provides one form of the perfect gas law. Another form is PV = nRT k where n is the number of moles and R is the universal gas constant. Obtain a relationship between r, R and the gas’ molecular weight M. PV = nRT k and P = ! rT k (see Eq. 5.2.1 and Appendix Eq A9.17) V = nRT k P = nR P P ! r " # \$ % & = nR ! r ( r = nR ! V m = ! V (massof gas) " r = nR m and M = m n (molecular weight) Therefore, r = R M or R = rM 2. Problem 5.2.1 in Kinsler et al. (a) P P o = ! ! o " # \$ % & ( = 1 + s ( ) ( ) 1 + ( s + ... = 1 + ( s for s<<1, that is, P = P o 1 + ! s ( ) = P o + P o ! s From (5.2.5) P ! P o = B " ! " o " o # \$ % & ( , P = P o + B ! " ! o ! o # \$ % & ( = P o + Bs , B = ! P o Also note from (5.2.6) p = Bs where B = !

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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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HW3_solution - ECE 473/TAM 413 Homework Assignment#3...

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