Solve this multiple-choice question and choose the correct option.

Concept/ApproachFor a point source emitting acoustic power P uniformly, the power spreads over the surface of a sphere 4πr2. Intensity I = P / (4πr2), hence I ∝ 1/r2. Step-by-stepI(r) = P / (4πr2)⇒ doubling r reduces I by a factor of 4. Common pitfallsConfusing amplitude (∝ 1/r) with intensity (∝ amplitude² ⇒ 1/r²). Final AnswerInversely proportional to r² (square of the distance)

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Acoustics and inverse-square law: How does sound intensity vary with distance from a point source? Assume an ideal point source radiating uniformly in all directions in free space; neglect absorption and reflections. Choose the correct proportionality statement.

Difficulty: Easy

Directly proportional to distance r
Inversely proportional to distance r
Inversely proportional to r² (square of the distance)
Independent of distance

Correct Answer: Inversely proportional to r² (square of the distance)

Explanation:

Concept/ApproachFor a point source emitting acoustic power P uniformly, the power spreads over the surface of a sphere 4πr². Intensity I = P / (4πr²), hence I ∝ 1/r².

Step-by-stepI(r) = P / (4πr²)⇒ doubling r reduces I by a factor of 4.

Common pitfallsConfusing amplitude (∝ 1/r) with intensity (∝ amplitude² ⇒ 1/r²).

Acoustics and inverse-square law: How does sound intensity vary with distance from a point source? Assume an ideal point source radiating uniformly in all directions in free space; neglect absorption and reflections. Choose the correct proportionality statement.

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