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

A string of length 40 cm and weighing 10 g is connected to a spring at one end and to a fixed wall at its other end. The spring possesses a spring constant of 160 N m ⁻¹ and is stretched by 1.0 cm . If a wave pulse is generated on the string near the wall, determine the time it will take to reach the spring.

Options

  1. A0.05 s
  2. B0.20 s
  3. C0.025 s
  4. D0.10 s

Correct answer

A. 0.05 s

Step-by-step solution

The tension in the string is provided by the restoring force of the stretched spring. T = kx = 160 0.01 = 1.6 N The linear mass density of the string is: = m L = 10 10⁻³ 40 10⁻² = 0.025 kg m ⁻¹ The speed of the transverse wave on the string is given by: v = T = 1.6 0.025 = 64 = 8 m s ⁻¹ The time taken by the wave pulse to travel the length of the string is: t = L v = 0.4 8 = 0.05 s

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