Question

The explosion of a fire cracker in the air at a height of 40 m produces a 100 dB sound level at ground below. What is the instantaneous total radiated power? Assuming that it radiates as a point source. (answer in Watts)

Answer 1

Given- $h=40m$ , loudness of sound , $L=100dB=10B$ ,

the intensity of sound is related with loudness , by the following relation ,

$I=I_0{10}^L$ , (where , $I_0={10}^{-12}$, threshold of hearing)

hence $I={10}^{-12}\times {10}^{10}={10}^{-2}W/m^2$ ,

now total radiated power due to point source on a sphere of radius $h$ ,

$P=I\times 4\pi h^2={10}^{-2}\times 4\times 3.14\times 40=5W$