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 first harmonic stationary wave is produced with a different frequency. What is the change in frequency and nature of displacement in 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 Option C is correct.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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