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 $27^{0} C$ 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 $27^{0} C$ is

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$350 m s^{- 1}$

$339 m s^{- 1}$

$300 m s^{- 1}$

$330 m s^{- 1}$

answer is B.

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Detailed Solution

The velocity of sound in air at $27^{0} C$ is

$v = 2 (n) [L_{2} - L_{1}]; where v =$ frequency of tuning fork and $L_{1}, L_{2}$ are the successive column length.

$∴ v = 2 \times 320 [73 - 20] \times 10^{- 2}$

$= 339.2 m s^{- 1} \approx 339 m s^{- 1}$

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