Question

If the sound level is 60 dB close to a speaker that has an area of $120c{m}^2$. The acoustic power output of the speaker is $12\times {10}^{-x}$ Watt. Find x.

Answer 1

We have loudness of sound ,

$L=log\left(I/I_0\right)$ ,

or $\left(I/I_0\right)={10}^L$ ,

given $L=60dB=6bel$ , and we know , $I_0={10}^{-12}W/m^2$ ,

therefore ,

$I/I_0={10}^6$ ,

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

now $A=120c{m}^2=120\times {10}^{-4}{m}^2$ ,

power output , $P=I\times A$ ,

so $P={10}^{-6}\times 120\times {10}^{-4}=1.2\times {10}^{-8}W$