In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air c

Question

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true? [2017]

Smart Achievers · Accepted Answer

(1, 2, 3)

According to question, the length of the air column is varied by changing the level of water in the resonance tube,

so, $(2 n + 1) \frac{λ}{4} = 50.7 + e . . . (i)$

and $(2 n + 3) \frac{λ}{4} = 83.9 + e . . . (i i)$

Dividing eq. (i) by (ii)

If $n = 1$ , $\frac{3 λ / 4}{5 λ / 4} = \frac{50.7 + e}{83.9 + e}$

$∴$ $3 \times 83.9 + 3 e = 5 \times 50.7 + 5 e$

$\Rightarrow 2 e = 1.8$ $∴$ $e = 0.9 cm$

$∴$ $\frac{3 λ}{4} = 50.7 + 0.9 = 51.6$

$\Rightarrow λ = 66.4 cm = 0.664 m$

Also speed of sound, $V = ν λ = 500 \times 0.664 {ms}^{- 1} = 332.0 {ms}^{- 1}$

Solution

1 The speed of sound determined from this experiment is 332 ${ms}^{- 1}$

2 The end correction in this experiment is 0.9 cm

3 The wavelength of the sound wave is 66.4 cm

4 The resonance at 50.7 cm corresponds to the fundamental harmonic

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