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Question

Sound with intensity larger than 120 dB appears painful 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?

A

40 cm

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B

80 cm

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C

120 cm

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D

10 cm

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Solution

The correct option is A

40 cm


Let's say the person can get to a closest distance of x.Then intensity at the distance I.

I = powersurface area=24πx2

Loudness, β = 10 log(II0) = 10 log (24πx2 × 1012)

|(I0 = 1.0 × 1012 ω m2)|

βmax = 120

120 = 10 log10(24πx2 × 1012)

x = 0.4m


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