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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?
Solution
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:
\[I = \frac{P}{4\pi r^2}\]
\[\left( \frac{2}{4\pi x^2} \right) = 1\]
\[\Rightarrow x^2 = \left( \frac{2}{4\pi} \right)\]
\[ \Rightarrow x = 0 . 4 m = 40 \text { cm }\]
Hence, the closest distance of the human ear from the small speaker is 40 cm.
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