In an experiment to determine the velocity of sound in air at room… | JEE Main 2022 (29 Jun, Shift 2)

Q77JEE Main 2022 · 29 JUN · SHIFT 2Medium

Organ Pipes & Resonance Tube

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms ${}^{-1}$ . The third resonance is observed when the air column has a length of _____________ cm.

Numerical answer type. Work it out, then open the answer.

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Answer: 104

$\lambda = \frac{336}{400} = 0.84$ m $= 84$ cm, so $\frac{\lambda}{4} = 21$ cm.
First resonance: $20 + e = 21 \Rightarrow e = 1$ cm.
Third resonance: $l_3 = \frac{5\lambda}{4} - e = 105 - 1 = 104$ cm
So the answer is 104 cm.

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