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Resonance in Sound Waves

In a resonanc...

Question

In a resonance tube with tuning fork of frequency $512 H z$ , first resonance occurs at water level equal to $30.3 c m$ and second resonance occurs at $63.7 c m$ . The maximum possible error in the speed of sound is

51.2 c m / s

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102.4 c m / s

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204.8 c m / s

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153.6 c m / s

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Solution

The correct option is C $204.8 c m / s$
$\begin{matrix} l_{1} + e = \frac{V}{4 f} \to (i) l_{2} + e = \frac{3 V}{4 f} \to (i i) S u b (i i) & (i) l_{2} - l_{1} = \frac{2 V}{4 f} l_{2} - l_{1} = \frac{V}{2 f} \frac{Δ (l_{2} - l_{1})}{l_{2} - l_{1}} = \frac{Δ V}{V} Δ V = 2 f Δ (l_{2} - l_{1}) = 2 f (Δ l_{1} + Δ l_{2}) . . . . . . f o r m a n e r r o r = 2 \times 512 \times (0.1 + 0.1) = 204.8 c m / s \end{matrix}$

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