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Standard XII

Physics

Resonance in Sound Waves

If a tuning f...

Question

If a tuning fork of frequency $(f_{0}) = 340 H z$ and tolerance $\pm 1 %$ is used in resonance column method, the first and the second resonance are measured at $ℓ_{1} = 24.0 c m a n d ℓ_{2} = 74.0 c m$ . Find maximum permissible error in speed of sound.

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1.2%

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1.4%

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1.8%

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Solution

The correct option is C 1.4%
$v = 2 f_{0} (ℓ_{2} - ℓ_{1}) \Rightarrow v = 340 m / s (\frac{Δ v}{v})_{m a x} = \frac{Δ f_{0}}{f_{0}} + \frac{Δ ℓ_{2} + Δ ℓ_{1}}{ℓ_{2} - ℓ_{1}} = \frac{1}{100} + \frac{0.1 + 0.1}{74.0 - 24.0} = 1.4 %$

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If a tuning fork of frequency (f0)=340 Hz and tolerance ±1% is used in resonance column method, the first and the second resonance are measured at ℓ1=24.0cm and ℓ2=74.0cm. Find maximum permissible error in speed of sound.

The correct option is C 1.4%v=2f0(ℓ2−ℓ1)⇒v=340m/s(Δvv)max=Δf0f0+Δℓ2+Δℓ1ℓ2−ℓ1=1100+0.1+0.174.0−24.0=1.4%

If a tuning fork of frequency $(f_{0}) = 340 H z$ and tolerance $\pm 1 %$ is used in resonance column method, the first and the second resonance are measured at $ℓ_{1} = 24.0 c m a n d ℓ_{2} = 74.0 c m$ . Find maximum permissible error in speed of sound.

The correct option is C 1.4%
$v = 2 f_{0} (ℓ_{2} - ℓ_{1}) \Rightarrow v = 340 m / s (\frac{Δ v}{v})_{m a x} = \frac{Δ f_{0}}{f_{0}} + \frac{Δ ℓ_{2} + Δ ℓ_{1}}{ℓ_{2} - ℓ_{1}} = \frac{1}{100} + \frac{0.1 + 0.1}{74.0 - 24.0} = 1.4 %$