Question

A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source. The ratio of amplitudes of the waves at P and Q is

• A. 3/2
• B. 9/4
• C. 2/3
• D. 4/9

Hint:

Amplitude is inversely proportional to the distance from the source ($A \propto 1/r$).

Answer 1

The Correct Option is B

Step 1: Intensity Relation
Intensity ($I$) follows the inverse square law: $I \propto \frac{1}{r^2}$.
Step 2: Amplitude Relation
Intensity is also proportional to the square of the amplitude ($A$): $I \propto A^2$. Thus, $A^2 \propto \frac{1}{r^2}$, which means $A \propto \frac{1}{r}$.
Step 3: Calculation
$\frac{A_P}{A_Q} = \frac{r_Q}{r_P} = \frac{9}{4}$.
Final Answer: (b)