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A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is

1. 330 m/s
2. 339 m/s
3. 300 m/s
4. 350 m/s

Correct answer: 339 m/s

Solution

The difference between two successive resonance lengths corresponds to half the wavelength of the sound wave. Thus, λ/2 = 73 cm - 20 cm = 53 cm, so λ = 106 cm = 1.06 m. Using v = fλ, where f = 320 Hz, we get v = 320 × 1.06 = 339.2 m/s ≈ 339 m/s.

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