Question

According to US government regulations, the maximum sound intensity level in the workplace is 90.0 dB. Within one factory, 32 identical machines produce a sound intensity level of 92.0 dB. How many machines must be removed to bring the factory into compliance with the regulation?

Answer 1

Answer:

12 machines

Explanation:

$I_0$ = Threshold of sound = $10^{-12}\ W/m^2$

$90=10log\dfrac{I}{I_0}\\\Rightarrow 9=log\dfrac{I}{10^{-12}}\\\Rightarrow 10^9=\dfrac{I}{10^{-12}}\\\Rightarrow I=10^9\times 10^{-12}\\\Rightarrow I=10^{-3}\ W/m^2$

$92=10log\dfrac{I}{I_0}\\\Rightarrow 9.2=log\dfrac{I}{10^{-12}}\\\Rightarrow 10^{9.2}=\dfrac{I}{10^{-12}}\\\Rightarrow I=10^{9.2}\times 10^{-12}\\\Rightarrow I=10^{-2.8}\ W/m^2$

One machine makes

$I_m=\dfrac{10^{-2.8}}{32}=0.0000495279122644\ W/m^2$

Number of machines

$n=\dfrac{10^{-3}}{\dfrac{10^{-2.8}}{32}}=20.19\approx 20\ machines$

Number of machines that are needed to be removed = 32-20 = 12 machines