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

As shown in the figure, two blocks, each with a mass of 3.2 kg , are connected by a wire CD . The entire system is suspended from the ceiling using another wire AB . The linear mass density of wire AB is 10 g m ⁻¹ , while that of wire CD is 8 g m ⁻¹ . Determine the speed of a transverse wave pulse produced in AB and in CD .

Options

  1. A56 m s ⁻¹ and 63 m s ⁻¹
  2. B79 m s ⁻¹ and 63 m s ⁻¹
  3. C79 m s ⁻¹ and 89 m s ⁻¹
  4. D63 m s ⁻¹ and 79 m s ⁻¹

Correct answer

B. 79 m s ⁻¹ and 63 m s ⁻¹

Step-by-step solution

Given: Mass of each block, m = 3.2 kg Linear mass density of wire AB , _ AB = 10 g m ⁻¹ = 0.01 kg m ⁻¹ Linear mass density of wire CD , _ CD = 8 g m ⁻¹ = 0.008 kg m ⁻¹ Acceleration due to gravity, g = 9.8 m s ⁻² The tension in wire CD is provided by the weight of the lower block: T_ CD = mg = 3.2 9.8 = 31.36 N The speed of the transverse wave pulse in CD is: v_ CD = T_ CD _ CD = 31.36 0.008 = 3920 62.6 m s ⁻¹ 63 m s ⁻¹ The tension in wire AB is provided by the weight of both blocks (neglecting the mass of the wires

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