Q79 / 160 · JIPMER 2007 · Physics

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

  • Correct answer
    A
    $9: 4$
  • B
    $2: 3$
  • C
    $3: 2$
  • D
    $4: 9$

Solution

The average power per unit area that is incident perpendicular to the direction of propagation is called the intensity. Intensity of sound $I=\frac{P}{4 \pi r^2}$ or, $I \propto \frac{1}{r^2}$ or, $\frac{I_1}{I_2}=\left(\frac{r_2}{r_1}\right)^2$ here, $r_1=2 \mathrm{~m}, r_2=3 \mathrm{~m}$ Substituting the values, we have $\frac{I_1}{I_2}=\left(\frac{3}{2}\right)^2=\frac{9}{4}$

Hence, the correct answer is option: 'A'.

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