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A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distance of 2 m and 3 m respectively from the source. The ratio of the intensities of the waves at P and Q is -
A
3 : 2
B
2 : 3
C
9 : 4
D
4 : 9
Detailed Solution
For a point source radiating power $P$ equally in all directions, the energy spreads over a sphere of area $4\pi r^2$.
Intensity $I = \dfrac{P}{4\pi r^2}$, so $I \propto \dfrac{1}{r^2}$.
$\dfrac{I_P}{I_Q} = \left(\dfrac{r_Q}{r_P}\right)^2 = \left(\dfrac{3}{2}\right)^2$
$\dfrac{I_P}{I_Q} = \dfrac{9}{4}$
So the ratio is 9 : 4.
Intensity $I = \dfrac{P}{4\pi r^2}$, so $I \propto \dfrac{1}{r^2}$.
$\dfrac{I_P}{I_Q} = \left(\dfrac{r_Q}{r_P}\right)^2 = \left(\dfrac{3}{2}\right)^2$
$\dfrac{I_P}{I_Q} = \dfrac{9}{4}$
So the ratio is 9 : 4.