Question

A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distances 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

Answer 1

The Correct Option is C

The question requires us to find the ratio of the intensities of sound at two points, P and Q, which are at distances of 2 meters and 3 meters, respectively, from a point source emitting sound uniformly in all directions. Let's solve this step by step.

Step 1: Understanding Intensity and Distance Relationship

The intensity of sound from a point source in an ideal situation is inversely proportional to the square of the distance from the source. Mathematically, this is represented by:

I \propto \frac{1}{r^{2}}

where \( I \) is the intensity and \( r \) is the distance from the source.

Step 2: Calculate Intensities at P and Q

Let the intensity at point P, which is 2 meters from the source, be \( I_P \), and intensity at point Q, which is 3 meters from the source, be \( I_Q \).

I_P \propto \frac{1}{(2)^{2}} = \frac{1}{4}

I_Q \propto \frac{1}{(3)^{2}} = \frac{1}{9}

Step 3: Calculate the Ratio of Intensities

The ratio of the intensities at P and Q is given by:

\frac{I_P}{I_Q} = \frac{\frac{1}{4}}{\frac{1}{9}} = \frac{9}{4}

Therefore, the ratio of the intensities at points P and Q is 9 : 4.

Conclusion

Given the relationship between intensity and distance from a point source, the correct answer is 9 : 4. Thus, the correct option is the last one.