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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

A

350 m/s

B

339 m/s

C

330 m/s

D

300 m/s

Step-by-Step Solution

The velocity of sound is given by v=2f(L2−L1)v = 2f(L_2 - L_1). Given f=320 Hzf = 320 \text{ Hz}, L1=20 cmL_1 = 20 \text{ cm}, L2=73 cmL_2 = 73 \text{ cm}. v=2×320×(73−20)×10−2=640×53×10−2=339.2 ms−1≈339 m/sv = 2 \times 320 \times (73 - 20) \times 10^{-2} = 640 \times 53 \times 10^{-2} = 339.2 \text{ ms}^{-1} \approx 339 \text{ m/s}.

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