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 the nature of displacement in air at the water surface?
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
Option C correctly suggests that the nature of displacement in the air at the water surface remains a node, and the frequency of the first harmonic stationary wave increases when more water is added to the cylinder. Adding more water increases the length of the air column, causing the frequency of the first harmonic stationary wave to increase. The water surface continues to act as a node, with minimal or zero displacement of air particles. Therefore, option c) is the correct choice.
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About Stationary Waves
Stationary waves form when two waves of the same frequency and amplitude travel in opposite directions and interfere. The topic covers nodes, antinodes, wavelength, phase, resonance, and the allowed frequencies on strings and in air columns. Unlike progressive waves, stationary waves do not transfer energy from one point to another.
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