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?

40 cm

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80 cm

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120 cm

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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.

$I = \frac{p o w e r}{s u r f a c e a r e a} = \frac{2}{4 π x^{2}}$

Loudness, $β = 10 l o g (\frac{I}{I_{0}}) = 10 l o g (\frac{2}{4 π x^{2}} \times 10^{12})$

$| (I_{0} = 1.0 \times 10^{- 12} ω m^{- 2}) |$

$β_{m a x} = 120$

$120 = 10 l o g_{10} (\frac{2}{4 π x^{2}} \times 10^{- 12})$

$x = 0.4 m$

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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?

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 × 10−12 ω m−2)| βmax = 120 120 = 10 log10(24πx2 × 10−12) x = 0.4m