Chapter 20: Problem 29

Question:        A certain loudspeaker (assumed to be a point source) emits $P = 31.6\ {\rm W}$ of acoustic power. A small microphone of effective cross sectional area $75.2\times 10^{-6}\ {\rm m^2}$ is located a distance $d=194.0\ {\rm m}$ from the loud speaker. Calculate

1.

the sound intensity at the microphone.

2.

the power incident on the microphone.

3.

the amount of energy that impinges on the microphone in $\Delta t = 25.0\ {\rm min}$.

Solution:        

$$I = {P\over 4\pi d^2} \ =\ {31.6\over 4\pi (194)^2} \ =\ 6.68\times 10^{-5}\ {\rm W/m^2} \ \ \ .$$ (3)

$$P_{\rm mic.} I . A \ =\ (6.68\times 10^{-5})(75.2\times 10^{-6})\ =\ 5.0\times 10^{-9}\ {\rm W} \ \ \ .$$ = (4)

$$E_{\rm mic.} P\ \Delta t \ =\ (5.0\times 10^{-9})(25 60)\ =\ 7.54\times 10^{-6}\ {\rm J} \ \ \ .$$ = (5)