To solve the problem it is necessary to apply the concepts related to sound intensity. The most common approach to sound intensity measurement is to use the decibel scale:
[tex]\beta (dB) = 10log_{10}(\frac{I}{I_0})[/tex]
Where,
[tex]I_0 = 1*10^{-12}[/tex] is a reference intensity. It is the lowest or threshold intensity of sound a person with normal hearing can perceive at a frequency of 1000 Hz.
I = Sound intensity
Our values are given by,
[tex]\beta = 104dB[/tex]
[tex]\#Autos = 7[/tex]
For each auto the intensity would be,
[tex]104 = 10log\frac{I}{1*10^{-12}}[/tex]
[tex]10.4= log_{10} (\frac{I}{10^{-12}})[/tex]
[tex]10^{10.4}*10^{-12}=I[/tex]
[tex]I = 0.02511W/m^2[/tex]
Therefore the sound intesity for the 7 autos is
[tex]I= 7* 0.02511[/tex]
[tex]I = 0.1748W/m^2[/tex]
The sound level for the 7 cars in dB is
[tex]\beta (dB) = 10log_{10}(\frac{0.1748}{1*10^{-12}})[/tex]
[tex]\beta (dB) = 112.42dB[/tex]
