In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tunin

Question

In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction. [2003]

Smart Achievers · Accepted Answer

(2)

$Let x be the end correction.$

$ℓ_{1} + x = \frac{λ}{4} or, λ = 4 (ℓ_{1} + x)$

$(ℓ_{2} + x) = \frac{3 λ}{4} or λ = \frac{4}{3} (ℓ_{2} + x)$

$∴$ $ν_{1} = \frac{v}{λ_{1}} = \frac{v}{4 (ℓ_{1} + x)}$

$∴$ $ν_{2} = \frac{v}{λ_{2}} = \frac{3 v}{4 (ℓ_{2} + x)}$

$Given ν_{1} = ν_{2}$

$∴$ $\frac{v}{4 (ℓ_{1} + x)} = \frac{3 v}{4 (ℓ_{2} + x)}$

$or, x = 0.025 m$

Solution

1 0.012 m

2 0.025 m

3 0.05 m

4 0.024 m

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