In a resonance tube with tuning fork of frequency 512 Hz, first resonance occurs at water level equal to 30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is [2005]

Question

In a resonance tube with tuning fork of frequency 512 Hz, first resonance occurs at water level equal to 30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is [2005]

Smart Achievers · Accepted Answer

(3)

In a resonance tube,

$ℓ_{1} + e = \frac{λ}{4}$ $ℓ_{2} + e = \frac{3 λ}{4}$

But $v = ν λ$

$∴$ $v = ν \frac{4}{3} (ℓ_{2} + e)$ $\Rightarrow ℓ_{2} + e = \frac{3 v}{4 ν} . . . (i)$

$∴$ $v = ν 4 (ℓ_{1} + e)$ $\Rightarrow ℓ_{1} + e = \frac{v}{4 ν} . . . (i i)$

Subtracting (i) and (ii),

$v = 2 ν (ℓ_{2} - ℓ_{1})$

$∴$ $Δ v = 2 ν (Δ ℓ_{2} + Δ ℓ_{1})$

$= 2 \times 512 \times (0.1 + 0.1) cm/s$

$= 204.8 cm/s$

Hence, maximum possible error in speed, $Δ v = 204.8 cm/s$

Solution

Q.
In a resonance tube with tuning fork of frequency 512 Hz, first resonance occurs at water level equal to 30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is [2005]

1 51.2 cm/s

2 102.4 cm/s

3 204.8 cm/s

4 153.6 cm/s

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