Question

The speed of a certain compression wave in air at standard temperature and pressure is 330 m/s. A point source of frequency 300 Hz radiates energy uniformly in all directions at the rate of 5 watt. The amplitude of the wave there is $1.15\times {10}^{-x}m$ . Find the value of x. [Density of air at $STP=1.29kg/m^3$]

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

now intensity , $I=2{\pi }^2{f}^2{A}^2\rho v$ ,

given $f=300Hz,v=330m/s,\rho =1.29kg/m^3$ ,

therefore ,

$A^2=I/\left(2{\pi }^2{f}^2\rho v\right)=\frac{9.95\times {10}^{-4}}{2\times {3.14}^2\times {300}^2\times 1.29\times 330}=1.31\times {10}^{-12}$ ,

$A=1.15\times {10}^{-6}m=1150nm$