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JEE Physics · Medium

Waves on String: Beats MCQ

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

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BeatsMediumQuestion 31362

Question

String of 64 cm gives 4 beats with a fork of 256 Hz. On shortening to 63.5 cm, beats decrease to 2. Frequency of string was:
  1. A
    252 Hz
  2. B
    260 Hz
    Correct
  3. C
    258 Hz
  4. D
    254 Hz

Correct answer

260 Hz

Explanation

Shortening increases f. Beats decrease → string was higher than fork. f_string = 256+4 = 260 Hz. Check: at 63.5 cm, f → higher still, beats should increase... actually: if string was 260 Hz and fork 256 Hz, beats = 4. Shortening raises string → 262 Hz, beats = 262−256 = 6 — increases. So string must be below fork: 256−4 = 252 Hz. Shortening → 254 Hz, beats = 256−254 = 2. ✓ Answer: 252 Hz.

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