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Standard VII

Physics

Intensity of Sound and Loudness

A loudspeaker...

Question

A loudspeaker at a rock concert generates $10^{- 2} W / m^{2}$ at $20 m$ at a frequency of $1 k H z$ . Assume that the speaker spreads its energy uniformly in three dimensions.
At what distance will the intensity be at the pain threshold of $1 W / m^{2}$ ?

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Solution

Since $I \propto \frac{1}{r^{2}}$

$\frac{I_{2}}{I_{1}} = (\frac{r_{1}}{r_{2}})^{2}$

$\frac{1}{10^{- 2}} = \frac{400}{x^{2}}$

$x = 2 m$

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A loudspeaker at a rock concert generates 10−2 W/m2 at 20 m at a frequency of 1 kHz. Assume that the speaker spreads its energy uniformly in three dimensions. At what distance will the intensity be at the pain threshold of 1 W/m2?

Since I∝1r2I2I1=(r1r2)2110−2=400x2x=2m

A loudspeaker at a rock concert generates $10^{- 2} W / m^{2}$ at $20 m$ at a frequency of $1 k H z$ . Assume that the speaker spreads its energy uniformly in three dimensions.
At what distance will the intensity be at the pain threshold of $1 W / m^{2}$ ?

Since $I \propto \frac{1}{r^{2}}$

$\frac{I_{2}}{I_{1}} = (\frac{r_{1}}{r_{2}})^{2}$

$\frac{1}{10^{- 2}} = \frac{400}{x^{2}}$

$x = 2 m$