First slide

Stationary waves

Question

If a tuning fork of frequency ( $340 \pm 1 %$ ) is used in the resonance tube method and the first and second resonance lengths are $20.0 cm$ and $74.0 cm$ respectively. Find the maximum possible percentage error in speed of sound.

Moderate

A

2.37%
B

3.37%
C

1.37%
D

0.37%

Solution

$l_{1} = 20.0 cm$
$Δ l_{1} = 0.1 cm$
$l_{2} = 74.0 cm$
$Δ l_{2} = 0.1 cm$
$\frac{Δ v}{v} \times 100 = \frac{Δ f}{f} \times 100 + (\frac{Δ l_{1} + Δ l_{2}}{l_{2} - l_{1}}) \times 100$
$= 1 % + (\frac{0.1 + 0.1}{74.0 - 20.0}) \times 100$
$= 1 % + 0.37 % = 1.37 %$

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