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MHT CET 2024 (11 May, Shift 1) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from MHT CET 2024 (11 May, Shift 1)

Q57MHT CET 2024 · 11 MAY · SHIFT 1Medium

Organ Pipes & Resonance Tube

A resonance tube closed at one end is of height 1.5 m. A tuning fork of frequency 340 Hz is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is (Neglect end correction, speed of sound in air $= 340\text{ m/s}$ )

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Answer: (d)

$\lambda = \frac{v}{n} = \frac{340}{340} = 1$ m.
Resonating air-column lengths: $\frac{\lambda}{4}, \frac{3\lambda}{4}, \frac{5\lambda}{4} = 25, 75, 125$ cm (all within 150 cm).
Minimum water height uses the longest air column: $150 - 125 = 25$ cm
So the answer is (d) 25 cm.

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