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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 . Assuming the wave travels in the positive x -direction and the end at x = 0 is at its positive extreme position at t = 0 , d

Options

  1. Ay = (1.0 cm ) 2 [ x 30 cm - t 0.01 s ]
  2. By = (1.0 cm ) 2 [ x 15 cm + t 0.005 s ]
  3. Cy = (1.0 cm ) 2 [ x 15 cm - t 0.005 s ]
  4. Dy = (1.0 cm ) 2 [ x 30 cm - t 0.01 s ]

Correct answer

D. y = (1.0 cm ) 2 [ x 30 cm - t 0.01 s ]

Step-by-step solution

The amplitude of the wave is given as A = 1.0 cm . Since the displacement of a particle in simple harmonic motion reaches zero twice in one complete cycle, the frequency f of the wave is: f = 200 2 = 100 Hz The time period T is: T = 1 f = 1 100 = 0.01 s The wave speed v is determined by the tension F and the linear mass density : v = F = 90 0.10 = 900 = 30 m s ⁻¹ = 3000 cm s ⁻¹ The wavelength is: = v f = 3000 100 = 30 cm The general equation for a wave travelling in the positive x -direction is: y(x,t) = A (2 ( x -

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