Question

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

• A. $24\mu J$
• B. $14\mu J$
• C. $34\mu J$
• D. $44\mu J$

Answer 1

The correct option is A $24\mu J$

The energy emitted by the speaker in one second is $3.0J$. Let us consider a sphere of radius 2 m centered at the speaker, the energy $3.0J$ falls normally on the total surface of this sphere in one second. The energy falling on the area $0.8c{m}^2$ of the microphone in one second.

=$\frac{0.8c{m}^2}{4\pi \left(4.0m^2\right)}\times 3.0J=4.8\times {10}^{-6}J$

The energy falling on the microphone in $5.0s$ is

$4.8\times {10}^{-6}J\times 5$
$=24\mu J$