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JEE Advanced 2008Paper 2
Exam
JEE Advanced
Year
2008
Paper
Paper 2
Subject
Physics
Chapter
Waves and Sound

JEE Advanced 2008 · Paper 2 · Physics · Waves and Sound

A vibrating string of certain length l under a tension T resonates...

A vibrating string of certain length ll under a tension TT resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm75 \mathrm{~cm} inside a tube closed at one end. The string also generates 4 beat/s when excited along with a tuning fork of frequency nn. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s340 \mathrm{~m} / \mathrm{s}, the frequency nn of the tuning fork (in Hz\mathrm{Hz} ) is

Options

  1. A344
  2. B336
  3. C117.3117.3
  4. D109.3109.3

Correct answer

A. 344

Step-by-step solution

With increase in tension, frequency of vibrating string will increase. Since number of beats are decreasing. Therefore, frequency of vibrating string or third harmonic frequency of closed pipe should be less than the frequency of tuning fork by 4 . ∴\therefore Frequency of tuning fork = Third harmonic frequency of closed pipe +4+4 =3(v4l)+\left(\frac{v}{4 l}\right)+4=3\left(\frac{340}{4 \times 0.75}\right)+4=3444=344\mathrm{~Hz} .\therefore correct option is (a).
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