JEE Physics · Hard

Waves on String: Melde's Experiment MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Melde's ExperimentHardQuestion 31352

Question

In Melde's transverse experiment, vibrator (200 Hz) makes string form 4 loops at tension T₁. At what tension T₂ will 5 loops form?
  1. A
    T₂ = 16T₁/25
    Correct
  2. B
    T₂ = 25T₁/16
  3. C
    T₂ = 4T₁/5
  4. D
    T₂ = 25T₁/16... is wrong

Correct answer

T₂ = 16T₁/25

Explanation

f = nv/(2L) = n√(T/μ)/(2L). Same f and L: n₁√T₁ = n₂√T₂. 4√T₁ = 5√T₂ → T₂/T₁ = 16/25. T₂ = 16T₁/25.