Question

g power output of 87 W. At what distance will the decibel reading be 120 dB, which is noise level of a loud indoor rock concert

Answer 1

Given that,

Output power = 87 W

Decibel reading = 120 dB

We need to calculate the intensity of sound

Using formula of intensity of sound

$dB=10\log(\dfrac{I}{I_{0}})$

Put the value into the formula

$120=10\log(\dfrac{I}{1\times10^{-12}})$

$12=log(\dfrac{I}{1\times10^{-12}})$

$10^{12}=\dfrac{I}{1\times10^{-12}}$

$I=10^{12}\times1\times10^{-12}$

$I=1\ W/m^2$

We need to calculate the distance

Using relation of power out[ut and intensity

$I=\dfrac{P}{4\pi r^2}$

Put the value into the formula

$1=\dfrac{87}{4\pi r^2}$

$r=\sqrt{\dfrac{87}{4\pi}}$

$r=2.63\ m$

Hence, The distance is 2.63 m