Question

A student is performing the experiment of resonance column. The diameter of the column tube is $6cm$. The frequency of the tuning fork is $504Hz$. Speed of the sound at the given temperature is $336m{s}^{-1}$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

A

$13cm$

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B

$14.8cm$

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C

$16.6cm$

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D

$18.4cm$

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Solution

The correct option is B $14.8cm$Step 1. Given dataDiameter of the column tube, $d=6cm$Frequency of the tuning fork, $f=504Hz$Velocity of the sound, $v=336m{s}^{-1}$Step 2. Finding the wavelength, $\lambda$By using the formula,$\lambda =\frac{v}{f}$$\lambda =\frac{336}{504}$$\lambda =66.66cm$Step 3. Finding the reading of the water level, $l$By using the formula, $l+e=\frac{\lambda }{4}$ [Where, $e$ is the end correction whose value is $0.6×radius$] $l+0.3d=\frac{66.66}{4}$ [Where $e=0.6×\frac{d}{2}=0.3d$]$l+0.3×6=16.66$ $l=14.8cm$Hence, the correct option is $\left(B\right)$.

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