Question

A straight line source of sound of length $L=10m$, emits a pulse of sound that travels radially outward from the source. What sound energy (in $mW$ ) is intercepted by an acoustic cylindrical detector of surface area $2.4c{m}^2$, located at a perpendicular distance $7m$ from the source? The waves reach perpendicularly at the surface of the detector. The total power emitted by the source in the form of sound is $2.2\times 10^{4}W$. (Use $\pi =22/7$ )

• A. 12
• B. 9
• C. 25
• D. 16

Answer 1

Answer: (A)

Imagine a cylinder of radius $7m$ and length $10m$.
Intensity of sound at the surface of cylinder is same everywhere.
Therefore $I=\frac{P}{2\pi rL}$
(As sound is propagating radially out only, sound energy does not flow out through the ends)
$\therefore I=50W/m^2$
Energy intercepted by the detector
$=I\times A=12mW$