Question

Intensity of sound at a point varies with distance from the source as:

• A. Directly proportional to the square of distance
• B. Directly proportional to distance
• C. Inversely proportional to the square of distance
• D. Inversely proportional to distance

Hint:

Recall the inverse square law that applies to any wave spreading out from a point source in three dimensions.

Answer 1

The Correct Option is C

Step 1: Sound spreads outward from a small source as a spherical wave, carrying a fixed total power P away from the source every second.

Step 2: At a distance r from the source, this power P is spread evenly over the surface of an imaginary sphere of radius r. The area of that sphere is \(4 \pi r^2\).

Step 3: Intensity is defined as power passing through unit area, so \(I = \dfrac{P}{4 \pi r^2}\).

Step 4: Since P stays constant, I is proportional to \(1/r^2\), which means intensity is inversely proportional to the square of the distance from the source.

Step 5: So as you move twice as far from a sound source, the intensity falls to one quarter, not to half. The correct choice is C.