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((I)/(I_(0)))`

Put the value into the formula

`120=10\log((I)/(1*10^(-12)))`

`12=log((I)/(1*10^(-12)))`

`10^(12)=(I)/(1*10^(-12))`

`I=10^(12)*1*10^(-12)`

`I=1\ W/m^2`

We need to calculate the distance

Using relation of power out[ut and intensity

`I=(P)/(4\pi r^2)`

Put the value into the formula

`1=(87)/(4\pi r^2)`

`r=\sqrt{(87)/(4\pi)}`

`r=2.63\ m`

Hence, The distance is 2.63 m