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JEE Main 2020 (8 Jan, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from JEE Main 2020 (8 Jan, Shift 1)

Q95JEE Main 2020 · 8 JAN · SHIFT 1Medium

Organ Pipes & Resonance Tube

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

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

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Answer: 105.75

$v = \sqrt{\frac{\gamma P}{\rho}} \propto \frac{1}{\sqrt{\rho}}$ , so in the gas $v' = \frac{300}{\sqrt{2}} \approx 212.1\text{ m/s}$ .
Open pipe: $f_n = \frac{nv'}{2L}$ , so $f_2 - f_1 = \frac{v'}{2L}$ .
$f_2 - f_1 = \frac{212.1}{2 \times 1} \approx 106\text{ Hz}$

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