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

By sinusoidally vibrating one end of a long horizontal string up and down, a travelling wave is generated. The vibration amplitude is 1.0 cm , and the displacement reaches zero 200 times per second. The string has a linear mass density of 0.10 kg m ⁻¹ and is maintained under a tension of 90 N . Find the speed and the wavelength of the wave.

Options

  1. A15 m s ⁻¹ , 30 cm
  2. B15 m s ⁻¹ , 15 cm
  3. C30 m s ⁻¹ , 30 cm
  4. D30 m s ⁻¹ , 15 cm

Correct answer

C. 30 m s ⁻¹ , 30 cm

Step-by-step solution

The speed of a transverse wave on a stretched string is given by the formula: v = T Substituting the given values of tension T = 90 N and linear mass density = 0.10 kg m ⁻¹ : v = 90 0.10 = 900 = 30 m s ⁻¹ In a sinusoidal wave, the displacement of any particle on the string becomes zero twice during each complete cycle. Since the displacement reaches zero 200 times per second, the frequency f of the wave is: f = 200 2 = 100 Hz The wavelength is related to the wave speed and frequency by the equation v = f . = v f =

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