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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 wavelength and the speed of the two travelling waves that can interfere to produce this vibration.

Options

  1. A20 cm and 120 m/s
  2. B10 cm and 30 m/s
  3. C20 cm and 60 m/s
  4. D30 cm and 60 m/s

Correct answer

C. 20 cm and 60 m/s

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 = 2A (kx) ( t) , we get: k = 0.314 cm ⁻¹ = 600 s ⁻¹ The wavelength is given by: = 2 k = 2 3.14 0.314 = 20 cm The speed v of the travelling waves is given by: v = k = 600 0.314 = 600 3.14 0.314 = 6000 cm/s = 60 m/s

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