A resonance tube is old and has jagged end. It is still used in the… | JEE Main 2019 (12 Jan, Shift 2)

Q105JEE Main 2019 · 12 JAN · SHIFT 2Difficult

Organ Pipes & Resonance Tube

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to:

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Answer: (b)

First resonance: $l + e = \frac{\lambda}{4} = \frac{v}{4f}$ ; the unknown end/reference offset $e$ is the same in both runs
Subtract: $l_2 - l_1 = \frac{v}{4}\left(\frac{1}{256} - \frac{1}{512}\right) = \frac{v}{2048}$
$0.27 - 0.11 = 0.16 = \frac{v}{2048} \Rightarrow v = 327.7\text{ m/s}$
So the answer is (b) $328\text{ m s}^{-1}$ .

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Organ Pipes & Resonance Tube question from JEE Main 2019 (12 Jan, Shift 2)

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