A source approaches the open end of a stationary pipe of length L with speed u and emits frequency fₛ. The far end is closed. Sound speed is v and f₀ is the pipe fundamental. Which combinations of u and fₛ produce resonance?
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Question

A source approaches the open end of a stationary pipe of length L with speed u and emits frequency fₛ. The far end is closed. Sound speed is v and f₀ is the pipe fundamental. Which combinations of u and fₛ produce resonance?

Select all that apply

G1 Physics · Accepted Answer

Step 1: For sound, f' = f(v ± vₒ)/(v ∓ vₛ), with velocities taken relative to the medium. Step 2: Choose signs for approach/recession; for an echo/reflection apply the Doppler shift twice. Step 3: If two frequencies are heard, take their difference for beats. Final: A: u = 0.8v, fₛ = f₀; D: u = 0.5v, fₛ = 1.5f₀.