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

A string, 2 m long and fixed at both ends, is set into vibrations in its first overtone. The wave speed on the string is 200 m s ⁻¹ and the amplitude is 0.5 cm . Determine the wavelength and the frequency.

Options

  1. A2 m , 100 Hz
  2. B4 m , 50 Hz
  3. C1 m , 200 Hz
  4. D4 3 m , 150 Hz

Correct answer

A. 2 m , 100 Hz

Step-by-step solution

For a string of length L fixed at both ends, the wavelength of the n -th harmonic is given by = 2L n . The first overtone corresponds to the second harmonic, so n = 2 . Substituting L = 2 m and n = 2 : = 2 2 2 = 2 m The frequency of the wave is given by f = v . Given the wave speed v = 200 m s ⁻¹ : f = 200 2 = 100 Hz

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