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The intensity of sound from a point source is $1 .0 \times 10^{- 8} W / m^{2}$ at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source? (in $\times 10^{- 10} W / m^{2}$ )

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Solution

Here $I_{1} = 1 .0 \times 10^{- 8} W / m^{2}$
$r_{1} = 5 .0 m, I_{2} = ?, r_{2} = 25 m$
We know that $I \propto (\frac{1}{r^{2}})$
$\begin{array}{l} I_{1} r_{1}^{2} = I_{2} r_{2}^{2} \\ I_{2} = \frac{I_{1} r_{1}^{2}}{r_{2}^{2}} = \frac{1 .0 \times 10^{- 8} \times 25}{625} = 4 .0 \times 10^{- 10} W / m^{2} \end{array}$

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Travelling wave

Remember concepts with our Masterclasses.

The intensity of sound from a point source is 1.0×10−8 W/m2 at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source? (in ×10−10 W/m2)

Here I1=1.0×10−8 W/m2 r1=5.0m, I2=?, r2=25 mWe know that I∝1r2I1r12=I2r22I2=I1r12r22=1.0×10−8×25625=4.0×10−10 W/m2

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The intensity of sound from a point source is $1 .0 \times 10^{- 8} W / m^{2}$ at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source? (in $\times 10^{- 10} W / m^{2}$ )