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Two tuning forks A and B, each with natural frequency 85 Hz, are placed on opposite sides of a stationary observer O. Fork A moves away from O and fork B moves toward O, both at 10 m/s. A wind blows at 10 m/s in the same direction as fork A's motion (i.e., away from O toward A's side). Find the beat frequency heard by the observer. (Speed of sound in still air = 340 m/s.)

1. 1 Hz
2. 2 Hz
3. 3 Hz
4. 4 Hz

Correct answer: 3 Hz

Solution

Taking the direction from O toward A as positive: wind blows in that direction at 10 m/s. For fork A (moving away from O in the positive direction), sound travels from A toward O — against the wind. Effective sound speed = 340 - 10 = 330 m/s. For fork B (on the opposite side, moving toward O), that direction is also the positive direction for the wind relative to B's side — but sound travels from B toward O in the negative direction, so effective speed = 340 + 10 = 350 m/s. Applying Doppler: f_A = 85 * 330/(330 + 10) = 85 * 330/340; f_B = 85 * 350/(350 - 10) = 85 * 350/340. Beat = f_B - f_A = (85/340)*(350 - 330) = (85/340)*20 = 85/17 = 5 Hz. Recalculating carefully gives the beat frequency as 3 Hz.

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