A cylindrical resonance tube, opened at both ends, has a fundamental frequency 'f' in air as shown in the given figure I.As shown in figure II, if half of the length is dipped vertically into water, then the fundamental frequency of the air column will become
Correct answer: D. 2f
- A. f/2
- B. f
- C. 3f/2
- D. 2f
Explanation
When a cylindrical resonance tube is opened at both ends, the fundamental frequency of the air column is directly proportional to the speed of sound in the air and inversely proportional to the wavelength of the sound wave. When half of the length of the air column is dipped into water, the effective length of the air column is halved, causing the fundamental frequency to double. Therefore, the correct answer is 2f. The other options are incorrect because they do not account for the change in frequency due to the alteration in the length of the air column.
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About Organ Pipes
Organ pipes produce standing sound waves in air columns, with resonance determined by whether each end is open or closed. The topic covers nodes, antinodes, fundamental frequency, harmonics, wavelength and end correction. Open pipes support all harmonics, while closed pipes support only odd harmonics under the ideal model.
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