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

The length of the wire between the pulleys, as shown in the figure, is 1.5 m , and its mass is 12.0 g . Determine the frequency of vibration when the wire vibrates in two loops, leaving the middle point of the wire between the pulleys at rest.

Options

  1. A35 Hz
  2. B70 Hz
  3. C105 Hz
  4. D140 Hz

Correct answer

B. 70 Hz

Step-by-step solution

Given: Length of the wire, L = 1.5 m Mass of the wire, m = 12.0 g = 12 10⁻³ kg Mass of the hanging blocks, M = 9 kg The linear mass density of the wire is: = m L = 12 10⁻³ 1.5 = 8 10⁻³ kg/m The tension in the wire is provided by the hanging mass (taking g = 9.8 m/s ^2 ): T = Mg = 9 9.8 = 88.2 N The speed of the transverse wave in the wire is: v = T = 88.2 8 10⁻³ = 11025 = 105 m/s Since the wire vibrates in two loops, there is a node at the center. The length of the wire corresponds to two half-wavelengths: L = 2 (

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