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Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, a path difference of 40 cm is equivalent to phase difference of 1.6π. The frequency of this wave is

1. 165 Hz
2. 150 Hz
3. 660 Hz
4. 330 Hz

Correct answer: 165 Hz

Solution

The phase difference (Δϕ) is related to the path difference (Δx) by the formula Δϕ = (2π/λ)Δx, where λ is the wavelength. Substituting Δϕ = 1.6π and Δx = 0.4 m, we get λ = 0.5 m. Using the wave equation v = fλ, where v = 330 m/s, we find f = v/λ = 330/0.5 = 165 Hz.

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