A student is performing the experiment of 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 \(336 \mathrm{~m} / \mathrm{s}\). The zero of the metre 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 :

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Waves & Sound

A student is performing the experiment of 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 m / s

. The zero of the metre 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)14.8 cm✓ Correct
(B)16.6 cm
(C)18.4 cm
(D)13 cm

Answer: (A)

Solution

At the first resonance the air column above the water carries a quarter of a wavelength, with the end correction

0.3 d

added to the measured length:

ℓ + 0.3 d = \frac{v}{4 f}

Here

v = 336

m/s

= 33600

cm/s and

f = 504

Hz, so

\frac{v}{4 f} = \frac{33600}{2016} = 16.67

cm, while

0.3 d = 0.3 \times 6 = 1.8

cm. Hence

ℓ = 16.67 - 1.8 = 14.87 cm

The metre scale reads zero at the top of the tube, so the water surface stands at the lower end of this air column and the scale reading there is

14.8

cm.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Waves & Sound

Solution

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