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 ?

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Solution

Here $I_{1} = 1.0 \times 10^{- 8} w_{1} / m^{2}, I_{2} = ?$

$r_{1} = 5.0 m, r_{2} = 25 m$

We know that,

$I \propto (\frac{1}{r^{2}})$

$\Rightarrow I_{1} r_{1}^{2} = I_{2} r_{2}^{2}$

$\Rightarrow I_{2} = \frac{I_{1} r_{1}^{2}}{r_{2}^{2}} = \frac{1.0 \times 10^{- 8} \times 25}{625}$

$= 4.0 \times 10^{- 10} W / m^{2}$

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The intensity of sound from a point source is 1.0×10−8Wm−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 ?

Here I1=1.0×10−8w1/m2,I2=? r1=5.0m,r2=25m We know that, I∝(1r2) ⇒I1r21=I2r22 ⇒I2=I1r21r22=1.0×10−8×25625 =4.0×10−10W/m2

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 ?