AS Daily A Level Physics question
A small loudspeaker emits sound equally in all directions in an open field. At a distance r, a microphone measures sound intensity I and pressure amplitude p. If the microphone is moved to 3r and air absorption is negligible, which statement must be true?
Answer
The correct answer is C.
Correct: C — Intensity becomes about I/9; pressure amplitude becomes about p/3. For a point-like source, intensity falls with 1/r^2, so at 3r it is I/9; since intensity ∝ (amplitude)^2, amplitude falls with 1/r, giving p/3. A states intensity falls only as 1/r, not 1/r^2, so it underestimates the drop in intensity. B applies the 1/r^2 drop to amplitude as well, ignoring that amplitude scales with the square root of intensity. C follows both inverse-square spreading and the amplitude–intensity relation correctly. D again assumes intensity falls as 1/r, and mixes the square-root relation with the wrong intensity scaling.