A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at length 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is:

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Solution

Q.
A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at length 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is: [2019]

1 500 m/s

2 156 m/s

3 344 m/s

4 172 m/s

Ans.
(3)

Frequency $(υ)$ = 800 Hz

As the pipe is closed at one end, so

$l_{3} - l_{2} = l_{2} - l_{1} = \frac{λ}{2} = 21.5$ $cm$

$∴$ $λ = 43.0$ $cm$

As $υ = \frac{v}{λ} \Rightarrow v = υ λ$

$∴$ $v = \frac{800 \times 43}{100} = 344$ $m$ $s^{- 1}$

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