An organ pipe of length T has one end closed but the other end open. What is the wavelength of the fundamental node emitted?
Correct answer: A. 4 × T
- A. 4 × T
- B. 2 × T
- C. 3 × T
- D. 1 × T
Explanation
The fundamental mode of a closed-open organ pipe produces a wavelength that is four times the length of the pipe. This is because the closed end is a displacement node and the open end is a displacement antinode, leading to a quarter wavelength fitting into the pipe length. Hence, the full wavelength is 4 times the pipe length, T. The other options do not account for the correct relationship between the pipe length and the wavelength in a closed-open pipe.
This question appeared on the ETEA MDCAT 2013 paper, which you can sit online with every answer explained.
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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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