A small speaker emits a sound wave uniformly in all directions. If the intensity of the sound wave it produces is I at a distance 3 meters away, then at 4 meters away the corresponding intensity is about

Question

BlackTom AI · Accepted Answer

Consider how sound intensity from a point source behaves: it spreads uniformly in all directions, and its intensity falls off with the square of the distance from the source (inverse square law).

Option 1: I/16. This would correspond to the intensity dropping by a factor of 16. Since distance increased from 3 m to 4 m, the factor should be (3/4)^2 = 9/16 ≈ 0.5625, not 1/16. Therefore I/16 is too small and incorrect.

Option 2: I/4. This would imply a drop by a factor of 4, which would occur if the distance increased by a factor of 2 (since (2)^2 = 4). The actual distance ratio is 4/3, whose square is 16/9 ≈ 1.78, not 4. Hence I/4 is not correct.

Option 3: 0.75I. This suggests only a 25% reduction from I, which would require a much smaller change in distance or a different propagation model. The inverse square law does not support such a small decrease when moving from 3 m to 4 m, so this is incorrect.

Option 4: 0.56I. Using the inverse square law, I4 = I3 × (r3^2 / r4^2) = I × (3^2 / 4^2) = I × (9/16) = 0.5625I ≈ 0.56I. This matches the expected prediction for a point source radiating uniformly and correctly reflects the distance increase from 3 m to 4 m.

In summary, the only option consistent with the inverse square dependence of intensity on distance for a point source is 0.56I, while the other options correspond to incorrect applications or misunderstandings of how intensity scales with distance.

Win25_PHYS010_10428 EC Quiz Ch.11-12

A small speaker emits a sound wave uniformly in all directions. If the intensity of the sound wave it produces is I at a distance 3 meters away, then at 4 meters away the corresponding intensity is about

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