AIIMS 2018 Physics Resonance in tubes MCQ Question
Vibrations are produced in a vertical tube of length 150 cm closed at one end by a tuning fork of frequency 340 Hz. Now water is filled slowly in the tube. If the speed of sound in air is 340 m/s then the minimum height of water required for resonance is
90 cm
75 cm
50 cm
25 cm
Correct Answer
Detailed Explanation
To achieve resonance in a closed tube, the length of the air column must correspond to an odd multiple of one-quarter wavelengths (λ/4). Given the speed of sound in air (v = 340 m/s) and the frequency of the tuning fork (f = 340 Hz), the wavelength (λ) can be calculated using the formula λ = v/f, resulting in λ = 1 m. The first resonance occurs when the length of the air column is λ/4, which is 0.25 m or 25 cm.
Options A (90 cm), B (75 cm), and C (50 cm) suggest heights that would correspond to higher harmonics, which are not achievable with the current setup as they exceed the maximum length of the tube (150 cm) and do not satisfy the resonance condition for a closed tube.
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