Question

A microphone of mass cross-sectional area $0.80{cm}^2$ is placed in front of a small speaker emitting $3.0W$ of sound output. If the distance between the microphone and the speaker is $2.0$ m, how much energy falls on the microphone in $5.0$ s?

Answer 1

Given,

Distance of the microphone from the speaker, $r=2m$

Power of sound Emitted by the speaker, $P_o=10\pi W$

Cross-sectional area of the microphone, $a=0.4c{m}^2=0.4\times {10}^{-4}{m}^2$

Sound emit from speaker is in hemispherical shape, Area of hemisphere, $A=2\pi r^2$

Calculate the intensity of sound.

Intensity of sound at distance 2m from speaker, $I=\frac{P_o}{A}=\frac{P_o}{2\pi r^2}=\frac{10\pi }{2\pi \times 2^2}$

Power of sound fall on microphone, $P_f=I\times a=\frac{10\pi }{2\pi \times 2^2}\times (0.4\times {10}^{-4})=5\times {10}^{-5}W$

Energy of sound fall on speaker in 5 second, $E=P_f\times time=(5\times {10}^{-5})\times 5=2.5\times {10}^{-4}J$