Question

The speed of a certain compressional wave in air at standard temperature and pressure is $330m/s$. A point source of frequency $300Hz$ radiates energy uniformly in all directions at the rate of $5watt$. The intensity of the wave at a distance of $20m$ from the source is $995\times {10}^{-x}W{m}^{-2}$. Find $x$.

Answer 1

The intensity $I$ of sound originated from a point source at a distance $r$ is given by ,

$I=P/A$ ,

where $A=4\pi r^2$ , area of sphere of radius $r$ ,

$P=$ power of source ,

given $P=5W,r=20m$ ,

therefore $I=5/\left(4\pi {20}^2\right)=5/(4\times 3.14\times 400)=9.95\times {10}^{-4}W/m^2$