A hollow pipe of length 0.8 m is closed at one end. At its open end… | MHT CET 2022 (11 Aug, Shift 2)

Q79MHT CET 2022 · 11 AUG · SHIFT 2Difficult

Organ Pipes & Resonance Tube

A hollow pipe of length $0.8\text{ m}$ is closed at one end. At its open end, a $0.5\text{ m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of pipe. If the tension in the string is $50\text{ N}$ and speed of sound in air is $320\text{ m/s}$ , the mass of the string is

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Answer: (a)

Pipe fundamental: $f = \frac{v}{4L} = \frac{320}{4 \times 0.8} = 100\text{ Hz}$
String 2nd harmonic: $f = \frac{2}{2l}\sqrt{\frac{T}{\mu}} = \frac{1}{0.5}\sqrt{\frac{50}{\mu}}$
$2\sqrt{\frac{50}{\mu}} = 100 \Rightarrow \mu = 0.02\text{ kg/m}$
Mass $= \mu l = 0.02 \times 0.5 = 0.01\text{ kg} = 10\text{ g}$
So the answer is (b) 10 g.

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Organ Pipes & Resonance Tube question from MHT CET 2022 (11 Aug, Shift 2)

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