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A Levels Physics (9702)•9702/13/M/J/20
Question 27 from 9702/13/M/J/20

Explanation

Resonance in a closed tube with adjusted length

Steps:

  • Initial setup: Tube acts as closed pipe at water surface; first resonance at fundamental frequency where length L = λ/4.
  • Frequency fixed after first resonance; louder sound indicates standing wave with node at water (closed end) and antinode at open end.
  • Water removal increases effective length L' to satisfy next resonance at same frequency: L' = 3λ/4.
  • New standing wave spans three quarter-wavelengths, with node at new water position and antinode at tube top.

Why C is correct:

  • Depicts 3λ/4 pattern with node at closed end (water) and two additional nodes/antinodes fitting closed-pipe overtone.

Why the others are wrong:

  • A: Shows λ/4 fundamental, unchanged from initial setup.
  • B: Indicates open-pipe pattern (λ/2), mismatched for closed end.
  • D: Displays higher harmonic (5λ/4) or incorrect node placement.

Final answer: C

Topic: Stationary waves

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