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

A heavy string is fastened at one end to a movable support and at the other end to a light thread, as shown in the figure. The light thread passes over a fixed pulley, suspending a weight that creates tension. The lowest resonant frequency of the heavy string is 120 Hz . The movable support is then pushed 10 cm to the right, causing the joint to rest on the pulley. Determine the new minimum frequency at which the hea

Options

  1. A60 Hz
  2. B120 Hz
  3. C480 Hz
  4. D240 Hz

Correct answer

D. 240 Hz

Step-by-step solution

Initially, the heavy string is fixed at the movable support and attached to a light thread at the other end. Since the light thread has negligible mass, it cannot support a transverse force. Therefore, the joint acts as a free end (an antinode) for the transverse waves in the heavy string. For a string of length L fixed at one end and free at the other, the lowest resonant (fundamental) frequency is given by: f₁ = v 4L = 120 Hz When the movable support is pushed 10 cm to the right, the entire heavy string shifts by

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