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

A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm ) [(0.314 cm ⁻¹) x] [(600 s ⁻¹)t] . Determine the length of the string.

Options

  1. A30 cm
  2. B10 cm
  3. C20 cm
  4. D60 cm

Correct answer

A. 30 cm

Step-by-step solution

The given equation of the standing wave is y = 0.4 (0.314 x) (600 t) . Comparing this with the standard equation of a standing wave y = A (kx) ( t) , we get: k = 0.314 cm ⁻¹ We know that the wave number k = 2 . 2 = 0.314 Using 3.14 , we have: 2 3.14 = 0.314 = 6.28 0.314 = 20 cm For a string fixed at both ends vibrating in its third harmonic, the length of the string L is given by: L = 3 2 Substituting the value of : L = 3 20 2 = 30 cm

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