Question

One physics professor talking produces a sound intensity level of 52 dB. It’s a frightening idea, but what would be the sound intensity level of 100 physics professors talking simultaneously?

Short answer

The intensity level of 100 professors talking simultaneously is 70dB

Step-by-step solution

Step 1. Write the given information.

A professor is talking

The intensity of the sound is $\beta$= 52dB

100 professors talk simultaneously.

Step 2. To determine the intensity of sound produced by 100 professors

The intensity of the sound is given by

$I=I_o\times {10}^{\beta /10dB}$

Here, I_o is the threshold hearing of humans. The average value is 1X10^-12 W/m².

Substitute the known values in the above expression

localid="1649072838046" $$\begin{gathered} I=(1\times {10}^{-12})\times {10}^{52dB/10dB} \\ I=1.5\times {10}^{-7}W/m^2 \end{gathered}$$

When 100 professors talk simultaneously, the intensity of the sound would become
$$\begin{gathered} I=100\times \left(1.5\times {10}^{-7}W/m^2\right) \\ I=1.5\times {10}^{-5}W/m^2 \end{gathered}$$

The intensity level is given by
$\beta =10dB{\log }_{10}\left(\frac{I}{I_o}\right)$
substitute the known values
$$\begin{gathered} \beta =10dB{\log }_{10}\left(\frac{1.5\times {10}^{-5}}{1\times {10}^{-12}}\right) \\ \beta =70dB \end{gathered}$$

Therefore, the intensity level produced by 100 professors is 70 dB