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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

A stretched string of length 1 m and mass 40 g is connected to a tuning fork. The tuning fork vibrates at 128 Hz in a direction perpendicular to the string. Determine the tension required in the string for it to vibrate in four loops.

Options

  1. A655 N
  2. B41 N
  3. C82 N
  4. D164 N

Correct answer

D. 164 N

Step-by-step solution

Given: Length of the string, L = 1 m Mass of the string, m = 40 g = 0.04 kg Linear mass density, = m L = 0.04 kg/m Frequency of the tuning fork, f = 128 Hz Number of loops, p = 4 Since the tuning fork vibrates perpendicular to the string in Melde's experiment, the frequency of the string is equal to the frequency of the tuning fork. The frequency of a stretched string vibrating in p loops is given by: f = p 2L T Substituting the given values: 128 = 4 2 1 T 0.04 128 = 2 T 0.04 64 = T 0.04 Squaring both sides: 4096 =

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