Answer:
The intensity of the sound is [tex]0.316W/m^2[/tex].
Explanation:
The equation for the decibel scale is
[tex]dB = 10 \:log(\dfrac{I}{I_n} )[/tex]
where [tex]I[/tex] is the intensity of sound, and [tex]I_n = 1*20^{-12}W/m^2[/tex] is the intensity of the least audible sound to the human ear.
Now, we are told that at a certain point the sound level is 115dB; therefore,
[tex]115dB = 10 \:log(\dfrac{I}{1*10^{-12}} )[/tex],
which we simplify and solve for [tex]I[/tex]as follows:
[tex]11.5 = log(\dfrac{I}{1*10^{-12}} )[/tex]
[tex]10^{11.5} = \dfrac{I}{1*10^{-12}}[/tex]
[tex]I =1*10^{-12}*10^{11.5}[/tex]
[tex]\boxed{I = 0.316W/m^2}[/tex]
which is the intensity of the sound at the point in question.
