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 50.7cm and 83.9 cm. Which of the following statements is (are) true?

Engineering

Physics

Quinkes Kundts and Resonance Tube Experiment

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 50.7cm and 83.9 cm. Which of the following statements is (are) true?

A

The speed of sound determined from this experiment is 332 m s^–1

B

The wavelength of the sound wave is 66.4 cm

C

The resonance at 50.7 cm corresponds to the fundamental harmonic

D

The end correction in this experiment is 0.9 cm

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$For (p + \frac{1}{2}) half loops$

$(p + \frac{1}{2}) \frac{λ}{2} = ℓ_{1}$

$\frac{(2 p + 1) λ}{4} = ℓ_{1} = 50 .7$ .....(1)

$For (p + \frac{3}{2}) half loops$

$(p + \frac{3}{2}) \frac{λ}{2} = ℓ_{2}$

$\frac{(2 p + 3) λ}{4} = ℓ_{2} = 83 .9$ .....(2)

Solving (1) & (2) λ = 66.4 cm

p = 1

$f = \frac{v}{λ} \Rightarrow v = 500 \times \frac{66 .4}{100} = 332 m / s$

So, option (A), (C)