Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 12 - Sound - Problems - Page 354: 19

Answer

135 dB

Work Step by Step

The intensity is given by equation 11–18, $I=2 \pi^2 \rho v f^2 A^2$. Using the density of air and the speed of sound in air, find the intensity. $$I=2 \pi^2 (1.29kg/m^3) (343m/s) (440Hz)^2 (0.00013m)^2=28.576W/m^2$$ $$\beta=10log\frac{I}{I_o}=10 log\frac{28.576W/m^2}{1.0\times10^{-12}W/m^2}\approx 135 dB$$ Ouch.
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