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A sonometer string vibrates in its 3rd overtone. The distance between the two bridges is 40 cm, the tension in the string is 90 N, and the mass per unit length is 100 g/m. What is the frequency of vibration?

1. 150 Hz
2. 112.5 Hz
3. 37.5 Hz
4. 75 Hz

Correct answer: 150 Hz

Solution

3rd overtone = 4th harmonic (overtone number = harmonic number - 1). Wave speed v = sqrt(T/mu) = sqrt(90 / 0.1) = sqrt(900) = 30 m/s. Frequency f = n * v / (2L) = 4 * 30 / (2 * 0.4) = 120 / 0.8 = 150 Hz.

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