Question

A siren creates a sound level of 60 dB at a location 500 m from the speaker. The siren is powered by a battery that delivers a total energy of 1.0 kJ. Assuming that the efficiency of siren is 30%, total time the siren can sound is $95\frac{x}{2}$. Find x.

Answer 1

Given - loudness of sound $L=60dB,r=500m,$ , input energy $E_{in}=1.0kJ=1000J$ ,

as the efficiency is $30$% ,therefore output energy (energy of siren) ,

$E_{out}=1000\times 30/100=300J$ ,

intensity of sound is given by ,

$I=I_0{10}^{L/10}$ , where $I_0={10}^{-12}W/m^2$ ,

hence $I={10}^{-12}\times {10}^{60/10}={10}^{-6}W/m^2$

but intensity at a distance is also given by ,

$I=P/4\pi r^2=E/(t\times 4\pi r^2)$ , where $P=power,t=time$ ,

or $t=E/(I\times 4\pi r^2)=\frac{300}{{10}^{-6}\times 4\times 3.14\times (500{)}^2}=95.5s$