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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 frequencies of the fundamental and the first two overtones.

Options

  1. A20 Hz , 60 Hz , 100 Hz
  2. B20 Hz , 40 Hz , 60 Hz
  3. C10 Hz , 30 Hz , 50 Hz
  4. D10 Hz , 20 Hz , 30 Hz

Correct answer

C. 10 Hz , 30 Hz , 50 Hz

Step-by-step solution

The linear mass density of the rope is given by: = m L = 80 10⁻³ 2.00 = 0.04 kg/m The speed of the transverse wave on the rope is: v = T = 256 0.04 = 6400 = 80 m/s The rope is fixed at one end, which acts as a node. The other end is tied to a light string (negligible mass), which provides no inertia and thus acts as a free end (antinode). The system behaves like a string fixed at one end and free at the other. The allowed frequencies (harmonics) for such a system are odd multiples of the fundamental frequency, give

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