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Question: The intensity of sound from a radio at a distance of 2 metres from its speaker is \(1 \times 0^{- 2}...

The intensity of sound from a radio at a distance of 2 metres from its speaker is 1×0−2μ 6muW⥂/⥂m2.1 \times 0^{- 2}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}. The intensity at a distance of 10 meters would be

A

0.2×10−2μ 6muW⥂/⥂m20.2 \times 10^{- 2}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}

B

1×10−2μ 6muW⥂/⥂m21 \times 10^{- 2}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}

C

4×10−4μ 6muW⥂/⥂m24 \times 10^{- 4}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}

D

5×10−2μ 6muW⥂/⥂m25 \times 10^{- 2}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}

Answer

4×10−4μ 6muW⥂/⥂m24 \times 10^{- 4}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}

Explanation

Solution

I∝1r2⇒I2I1=r12r22I \propto \frac{1}{r^{2}} \Rightarrow \frac{I_{2}}{I_{1}} = \frac{r_{1}^{2}}{r_{2}^{2}}⇒ I21×10−2=22102=4100\frac{I_{2}}{1 \times 10^{- 2}} = \frac{2^{2}}{10^{2}} = \frac{4}{100}

⇒ I2=4×10−2100I_{2} = \frac{4 \times 10^{- 2}}{100} = 4×10−4 6muμ 6muW⥂/⥂m24 \times 10^{- 4}\mspace{6mu}\mu\mspace{6mu} W ⥂ / ⥂ m^{2}