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

A rope of length 2.00 m and mass 80 g is fixed at one end and tied to a light string at the other end. The tension in the string is 256 N . Determine the wavelengths corresponding to the fundamental and the first two overtones.

Options

  1. A8.00 m , 4.00 m , 2.67 m
  2. B8.00 m , 2.67 m , 1.60 m
  3. C4.00 m , 2.00 m , 1.33 m
  4. D2.00 m , 0.67 m , 0.40 m

Correct answer

B. 8.00 m , 2.67 m , 1.60 m

Step-by-step solution

The rope is fixed at one end and tied to a light string at the other end. The fixed end acts as a node and the end tied to the light string acts as a free end (antinode). For a string fixed at one end and free at the other, the length L is related to the wavelength by: L = (2n + 1) 4 for n = 0, 1, 2, The allowed wavelengths are given by: = 4L 2n + 1 Given L = 2.00 m . For the fundamental mode ( n = 0 ): ₀ = 4 2.00 1 = 8.00 m For the first overtone ( n = 1 ): ₁ = 4 2.00 3 = 8.00 3 2.67 m For the second overtone ( n

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