A2 Daily A Level Physics question
Two identical loudspeakers are driven in phase at frequency f0 in a large hall. At a fixed listening point P the distances to the speakers differ by 1.5 m, and a deep minimum in sound intensity is heard at P. You now slowly increase only the frequency while nothing else moves. By approximately what percentage must the frequency increase from f0 to reach the first maximum at P?
Answer
The correct answer is C.
Correct: C — Increase by about 33%. At the minimum, Δ = 1.5λ0. The next maximum on increasing frequency requires Δ = 2λ′, so λ′ = (1.5/2)λ0 = 0.75λ0. Since frequency is inversely proportional to wavelength at fixed wave speed, f′ = f0/0.75 ≈ 1.33f0, i.e. a 33% increase. A Confuses the 25% decrease in wavelength (from λ0 to 0.75λ0) with the percentage increase in frequency; because f ∝ 1/λ, a 25% drop in λ corresponds to a 33% rise in f, not 25%. B Treats the +0.5 shift in Δ/λ from 1.5 to 2 as implying a 50% frequency increase; however the required wavelength change is to 0.75λ0, giving +33% in f, not +50%. C This correctly uses λ′ = Δ/2 and f ∝ 1/λ to get f′/f0 = 1/0.75 ≈ 1.33. D Greatly overestimates the needed change, as if moving to a more distant maximum or mis-scaling frequency with the integer order; the nearest maximum on increasing f only requires f to rise by 33%, not 67%.