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organ pipe and resonance tube questions with solutions

Practice Wave Motion for JEE Main, JEE Advanced, NEET, and Classes 11–12. Attempt each question, then open it for the full solution.

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NumericmediumWave Motion
A pipe closed at one end has geometrical length 0.84 m. The end correction at its single open end is 1 cm. If the speed of sound is 340 m/s and the fundamental frequency is N Hz, find N.
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NumericmediumWave Motion
An organ pipe open at both ends has geometrical length 0.98 m. The end correction at each open end is 1 cm. If the speed of sound is 340 m/s, and the fundamental frequency is N Hz, find N.
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NumericmediumWave Motion
An organ pipe resonates at 400 Hz in a fixed mode when the gas inside it is at 300 K. The same gas is heated to 363 K without changing the pipe dimensions or the mode. If the new resonance frequency is N Hz, find N.
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MCQeasyWave Motion
An organ pipe has geometrical length L, and the end correction for each open end is e. Which pair correctly gives the effective length of an open pipe and a pipe closed at one end?
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MCQmediumWave Motion
A resonance tube of circular cross-section is used with a 500 Hz tuning fork. The speed of sound is 340 m/s and the first resonance occurs when the measured air-column length is 16.4 cm. Using the approximation e = 0.6r, where r is the tube radius, what is the tube radius?
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NumericmediumWave Motion
A 500 Hz tuning fork produces two successive resonances in a resonance tube at air-column lengths 16 cm and 50 cm. Assuming the same end correction at both resonances, if the speed of sound is N m/s, find N.
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A/RmediumWave Motion
Choose the correct option for the following Assertion (A) and Reason (R).
Assertion
The difference between two successive resonance lengths in the same resonance tube does not depend on the end correction.
Reason
The same end correction is added to both effective resonance lengths and therefore cancels when the two resonance conditions are subtracted.
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A/RmediumWave Motion
Choose the correct option for the following Assertion (A) and Reason (R).
Assertion
An ideal open organ pipe can support the second harmonic, whereas an ideal organ pipe closed at one end cannot support the second harmonic.
Reason
An open organ pipe allows all integral harmonics, whereas a pipe closed at one end allows only odd multiples of its fundamental frequency.
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NumericmediumWave Motion
The first two resonance lengths of a resonance tube are 15.0 cm and 46.2 cm. The end correction is related to the tube radius r by e = 0.6r. If the tube radius is N cm, find N.
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MCQmediumWave Motion
A resonance tube acts as a pipe closed at the water surface and open at the top. For a tuning fork of fixed frequency, two successive resonance air-column lengths are l₁ and l₂. Assuming the end correction is the same for both resonances, which relation is correct?
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