Pain In The Ears
Classical Mechanics
Level
4
Sound with intensity larger than 120db appears painful to a person. A small speaker delivers 2.0W of audio-output. How close can the person get to the speakers without hurting his ears?
The correct answer should be in cm.
The answer is 40.
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1 solution
Loudness=10log(Intensity/max Intensity); max audible intensity=10^-12 W/m^2. Intensity=1 W/m^2. If we treat the speaker as a point source,then sound spreads as a spherical core. At a distance r,from speakers the intensity. I=P/4pir^2 or r=(P/4pil)^1/2=(2W/4piWm^-2)^1/3 r=(I/2pi)^1/2 m which is nearly 0.4 m=40 cm.