A stationary source and a stationary reflecting wall lie on opposite sides of an observer. The source emits frequency f. The observer moves towards the wall with speed u, so the direct wave reaches the observer from behind while the reflected wave reaches from ahead. What is the beat frequency heard by the observer?
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Question

A stationary source and a stationary reflecting wall lie on opposite sides of an observer. The source emits frequency f. The observer moves towards the wall with speed u, so the direct wave reaches the observer from behind while the reflected wave reaches from ahead. What is the beat frequency heard by the observer?

Options

G1 Physics · Accepted Answer

For the direct wave, the observer moves in the same direction as the wave and therefore away from the source: f₁ = f×(v−u)/v. For the reflected wave, the observer moves towards the incoming wave: fᵣ = f×(v+u)/v. Hence, fᵦ = fᵣ−f₁ = f[(v+u)−(v−u)]/v = 2f×u/v. Correct option: B.