A point source emits sound equally in all direction in a non-absorbing medium. Two points P and Q are at distance of 2m and 3m respectively from the source. The ratio of the intensities of the wave at P and Q is.

Question

A point source emits sound equally in all direction in a non-absorbing medium. Two points P and Q are at distance of 2m and 3m respectively from the source. The ratio of the intensities of the wave at P and Q is. (A) 9:4 (B) 2:3 (C) 3:2 (D) 4:9

Tardigrade Admin · Accepted Answer

The average power per unit area that is incident perpendicular to the direction of propagation is called the intensity, i.e.,

I = \frac{P}{4 π r ^{2}}

Or

I \propto \frac{I}{r ^{2}}

Or

\frac{I _{2}}{I _{2}} = (\frac{r _{2}}{r _{1}})^{2}

Here,

r_{1} = 2 m, r_{2} = 3 m

∴ \frac{I _{1}}{I _{2}} = (\frac{3}{2})^{2} = \frac{9}{4}

Q. A point source emits sound equally in all direction in a non-absorbing medium. Two points P and Q are at distance of 2m and 3m respectively from the source. The ratio of the intensities of the wave at P and Q is.

9:4

2:3

3:2

4:9

The average power per unit area that is incident perpendicular to the direction of propagation is called the intensity, i.e., I=4πr2P​ Or I∝r2I​ Or I2​I2​​=(r1​r2​​)2 Here, r1​=2m,r2​=3m ∴I2​I1​​=(23​)2=49​

Q. A point source emits sound equally in all direction 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 wave at $P$ and $Q$ is.