Given that,
Output power = 87 W
Decibel reading = 120 dB
We need to calculate the intensity of sound
Using formula of intensity of sound
[tex]dB=10\log(\dfrac{I}{I_{0}})[/tex]
Put the value into the formula
[tex]120=10\log(\dfrac{I}{1\times10^{-12}})[/tex]
[tex]12=log(\dfrac{I}{1\times10^{-12}})[/tex]
[tex]10^{12}=\dfrac{I}{1\times10^{-12}}[/tex]
[tex]I=10^{12}\times1\times10^{-12}[/tex]
[tex]I=1\ W/m^2[/tex]
We need to calculate the distance
Using relation of power out[ut and intensity
[tex]I=\dfrac{P}{4\pi r^2}[/tex]
Put the value into the formula
[tex]1=\dfrac{87}{4\pi r^2}[/tex]
[tex]r=\sqrt{\dfrac{87}{4\pi}}[/tex]
[tex]r=2.63\ m[/tex]
Hence, The distance is 2.63 m
