Question

Sound with intensity larger than 120 dB appears pain full to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?

Answer 1

Given:
The sound level that can hurt the human ear is 120 dB. Then, the intensity I is 1 W/m².
Audio output of the small speaker P = 2 W
Let the closest distance be x.
We have:
$$\begin{gathered} I=\frac{P}{4\pi r^2} \\ \left(\frac{2}{4\mathrm{\pi }{x}^2}\right)=1 \end{gathered}$$
$$\begin{gathered} \Rightarrow x^2=\left(\frac{2}{4\mathrm{\pi }}\right) \\ \Rightarrow x=0.4\mathrm{m}=40\mathrm{cm} \end{gathered}$$

Hence, the closest distance of the human ear from the small speaker is 40 cm.