First slide

Experiments to find speed of sound

Question

In the experiment for the determination of the speed of sound in air using the resonance column, it is observed that 0.1 m of air column resonates with a tuning fork in the fundamental mode. When the length of the air column is changed to 0.35 m, the same tuning fork resonates with the first overtone. What is the end correction ?

Moderate

A

0.0125 m
B

0.025 m
C

0.05 m
D

0.075 m

Solution

$v = v_{1}^{} = \frac{1}{4 (L_{1}^{} + e)} \sqrt{\frac{γ P}{ρ}} (i)$ Let v be the frequency of the tuning fork and e the end correction. Given $v = v_{1}^{} = \frac{1}{4 (L_{1}^{} + e)} \sqrt{\frac{γ P}{ρ}} (i)$
$v = v_{3}^{} = \frac{3}{4 (L_{2}^{} + e)} \sqrt{\frac{γ P}{ρ}} (i i)$
Equating (i) and (ii), we get
$\frac{1}{L_{1}^{} + e} = \frac{3}{L_{2}^{} + e}$
OR $\frac{1}{0.1 + e} = \frac{3}{0.35 + e}$
Which gives e = 0.025 m. Hence the correct choice is (b).

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