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Three musicians demonstrate the Doppler effect. Musician A rides in a car at speed u directly away from stationary Musician B. Musician C rides in a car toward B at the same speed u. A plays note at frequency f_A. B hears this note, adjusts his instrument, and plays the same frequency he heard. (A) The note C hears coming from B has the same pitch as f_A. (B) The note A hears coming from B is higher in pitch than f_A. (C) The note A hears coming from B is lower in pitch than f_A. (D) The note B hears coming from A is lower in pitch than f_A.

1. The note C hears coming from B has the same pitch as f_A.
2. The note A hears coming from B is higher in pitch than f_A.
3. The note A hears coming from B is lower in pitch than f_A.
4. The note B hears coming from A is lower in pitch than f_A.

Correct answer: The note B hears coming from A is lower in pitch than f_A.

Solution

Step 1: B hears A (A moving away at u): f_B = f_A * v/(v+u). Since v+u > v, f_B < f_A -> D is correct (B hears lower pitch). Step 2: B plays f_B. C moves toward B at u: C hears f_C = f_B * (v+u)/v = f_A*v/(v+u)*(v+u)/v = f_A -> A is correct (C hears same pitch as f_A). Step 3: A moves away from B, B plays f_B. A hears: f_A_hears = f_B*(v-u)/v = f_A*(v-u)/(v+u) < f_A -> C is correct (A hears lower pitch, not higher, so B is wrong). Correct statements: A, C, D. The most directly verifiable single answer here is D.

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