Question

At the race track, one race car starts its engine with a resulting intensity level of 104.0 dB at point P. Then 6 more cars start their engines. If the other 6 cars each produce the same intensity level at point P as the first car, what is the new intensity level with all 7 cars running?

Answer 1

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:

$\beta (dB) = 10log_{10}(\frac{I}{I_0})$

Where,

$I_0 = 1*10^{-12}$ 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,

$\beta = 104dB$

$\#Autos = 7$

For each auto the intensity would be,

$104 = 10log\frac{I}{1*10^{-12}}$

$10.4= log_{10} (\frac{I}{10^{-12}})$

$10^{10.4}*10^{-12}=I$

$I = 0.02511W/m^2$

Therefore the sound intesity for the 7 autos is

$I= 7* 0.02511$

$I = 0.1748W/m^2$

The sound level for the 7 cars in dB is

$\beta (dB) = 10log_{10}(\frac{0.1748}{1*10^{-12}})$

$\beta (dB) = 112.42dB$