Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson

Chapter 20 - Traveling Waves - Exercises and Problems: 71

Answer

Each therapy session should last 21 minutes.

Work Step by Step

We can find the intensity of the sound waves. $I = I_0~10^{(\beta/10)}$ $I = (10^{-12}~W/m^2)~10^{(93/10)}$ $I = 2.0\times 10^{-3}~W/m^2$ We can find the area of the hemisphere. $A = \frac{1}{2}(4\pi~R^2)$ $A = 2\pi~R^2$ $A = (2\pi)(0.080~m)^2$ $A = 0.040~m^2$ We can find the power received by the hemisphere. $P = I~A$ $P = (2.0\times 10^{-3}~W/m^2)(0.040~m^2)$ $P = 8.0\times 10^{-5}~W$ We can find the number of seconds required to reach a total energy of 0.10 J. $t = \frac{E}{P}$ $t = \frac{0.10~J}{8.0\times 10^{-5}~W}$ $t = 1250~s$ We can convert the time to minutes. $t = (1250~s)(\frac{1~min}{60~s}) = 21~minutes$ Each therapy session should last 21 minutes.

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