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Given: Wavelength of first wave (λ1) = 50 cm = 0.5 m. Wavelength of second wave (λ2) = 51 cm = 0.51 m. Frequency of beats per sec (n) = 12. What is the velocity of sound?

1. 306 m/s
2. 320 m/s
3. 330 m/s
4. 340 m/s

Correct answer: 330 m/s

Solution

The beat frequency is given by the difference in frequencies of the two waves: n = |f1 - f2|. Using the relation v = fλ, we find f1 = v/λ1 and f2 = v/λ2. Substituting these into the beat frequency equation, we get n = v(1/λ1 - 1/λ2). Solving for v using n = 12, λ1 = 0.5 m, and λ2 = 0.51 m, we find v = 330 m/s.

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