A first harmonic stationary sound wave is produced in the air of a cylinder that is half-filled with water. More water is added to the cylinder. Now the first harmonic stationary wave is produced with a different frequency. What are the changes in frequency and the nature of displacement in the air at the water surface?
Correct answer: B. Nature of displacement = antinode, 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
b) Nature of displacement = antinode, change in frequency = increase:This option is correct. When more water is added to the cylinder, the effective length of the air column decreases, leading to an increase in the frequency of the first harmonic stationary wave. The antinode at the water surface remains unchanged as it is a region of maximum displacement.
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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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