Q 11-14-085JEE MainJEE Main 2021 (25 Feb, Shift 1)Medium
A student is performing the experiment of the resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is $336\ \text{m s}^{-1}$. 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:
Answer: (A) 14.8 cm
$\lambda = \dfrac{336}{504} = 0.667$ m, so $\dfrac{\lambda}{4} = 16.67$ cm.
With end correction $e = 0.3d = 0.3\times6 = 1.8$ cm, first resonance occurs when $l + e = \dfrac{\lambda}{4}$:
$$l = 16.67 - 1.8 \approx 14.8\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics