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 - General Problems - Page 357: 75

Answer

14 watts.

Work Step by Step

Use the definition of sound level. The change in sound level depends logarithmically on the increase in intensity, and thus, on the emitted power. $$\beta = 10log \frac{I_f}{I_o} $$ $$\Delta \beta = 10log \frac{I_f}{I_o}-10log \frac{I_i}{I_o}=10log \frac{I_f}{I_i} $$ Use the given information. $$ -12dB=10log\frac{P_{15\;kHz}}{225\;W} $$ $$ -1.2=log\frac{P_{15\;kHz}}{225\;W} $$ $$ 10^{-1.2}= \frac{P_{15\;kHz}}{225\;W} $$ $$ P_{15\;kHz}=(10^{-1.2})225\;W=14\;W $$
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