A first harmonic stationary sound wave is produced in the air of the cylinder, which is half filled with water. More water is added to the cylinder and now the first harmonic stationary wave is produced with a different frequency. What is the change in frequency and nature of displacement in the air at the surface of the water?
Correct answer: C. Nature of displacement = node change in frequency = increase
- A. Nature of displacement = antinode change in frequency = decrease
- B. Nature of displacement = antinode change in frequency = increase
- C. Nature of displacement = node change in frequency = increase
- D. Nature of displacement = node change in frequency = decrease
Explanation
Since the cylinder is half filled with water, we can treat this as a pipe where it is closed on one end and open on the other. The closed end is a node. Adding water would decrease the original length, change the node and increase the frequency as the formula for frequency is F = v / 2L and since the length is decreasing, the frequency is increasing.Hence, C is the correct option
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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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