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

A steel wire with a mass of 4.0 g and a length of 80 cm is fixed at both its ends. The tension in the wire is 50 N . Determine the frequency and wavelength of the fourth harmonic of the fundamental.

Options

  1. A250 Hz , 40 cm
  2. B62.5 Hz , 160 cm
  3. C500 Hz , 20 cm
  4. D125 Hz , 80 cm

Correct answer

A. 250 Hz , 40 cm

Step-by-step solution

Linear mass density of the wire is = m L = 4.0 10⁻³ 0.8 = 5.0 10⁻³ kg/m The speed of the transverse wave on the string is v = T = 50 5.0 10⁻³ = 100 m/s For a string fixed at both ends, the frequency of the n -th harmonic is given by f_n = nv 2L For the fourth harmonic, n = 4 f₄ = 4 100 2 0.8 = 250 Hz The wavelength of the n -th harmonic is given by _n = 2L n ₄ = 2 80 4 = 40 cm

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