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.
IIT JEE
Physics
Difficulty: Easy
Choose an option
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ADirectly proportional to distance r
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BInversely proportional to distance r
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CInversely proportional to r² (square of the distance)
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DIndependent of distance
Answer
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).
Final AnswerInversely proportional to r² (square of the distance)