Question

The noise level in a classroom in absence of the teacher is 50 dB when 50 students are present. Assuming that on the average each student output same sound energy per second, what will be the noise level if the number of students is increased to 100?

Answer 1

Let the intensity of each student be I and the sound level of 50 students be ${\beta }_1$. If the number of students increases to 100, the sound level becomes ${\beta }_2$.
Using $\beta =10{\log }_{10}\left(\frac{I}{I_0}\right)$,
where I₀ is the constant reference intensity, I is the intensity and β is the sound level.
$$\begin{gathered} {\beta }_1=10{\log }_{10}\left(\frac{50I}{I_0}\right) \\ {\beta }_2=10{\log }_{10}\left(\frac{100I}{I_0}\right) \end{gathered}$$
$$\begin{gathered} \Rightarrow {\beta }_2-{\beta }_1=10{\log }_{10}\left(\frac{100\mathrm{I}}{{\mathrm{I}}_0}\right)-10{\log }_{10}\left(\frac{50\mathrm{I}}{{\mathrm{I}}_0}\right) \\ =10{\log }_{10}\left(\frac{100\mathrm{I}}{50\mathrm{I}}\right) \\ =10{\log }_{10}\left(2\right) \\ =3 \end{gathered}$$

Therefore, the noise level of 100 students $\left({\beta }_2\right)$ will be = 50+3 = 53 dB.