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/Approach
For 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-step
I(r) = P / (4πr²)⇒ doubling r reduces I by a factor of 4.

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

Final Answer
Inversely 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.

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