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

A wave propagates along the positive x -direction with a speed of 20 m s ⁻¹ . The amplitude of the wave is 0.20 cm and the wavelength is 2.0 cm . Which of the following is a possible wave equation that describes this wave?

Options

  1. Ay = (0.20 cm ) [(2 cm ⁻¹)x - ( 10^3 s ⁻¹)t]
  2. By = (0.20 cm ) [(2 cm ⁻¹)x + ( 10^3 s ⁻¹)t]
  3. Cy = (0.20 cm ) [( cm ⁻¹)x - (2 10^3 s ⁻¹)t]
  4. Dy = (0.20 cm ) [( cm ⁻¹)x + (2 10^3 s ⁻¹)t]

Correct answer

C. y = (0.20 cm ) [( cm ⁻¹)x - (2 10^3 s ⁻¹)t]

Step-by-step solution

The amplitude of the wave is A = 0.20 cm . The wavelength is = 2.0 cm . The wave number k is given by k = 2 = 2 2.0 cm = cm ⁻¹ . The wave speed is v = 20 m s ⁻¹ = 2000 cm s ⁻¹ . The angular frequency is given by = kv = ( cm ⁻¹)(2000 cm s ⁻¹) = 2 10^3 s ⁻¹ . For a wave propagating in the positive x -direction, the equation is of the form y = A (kx - t) . Substituting the values, we get y = (0.20 cm ) [( cm ⁻¹)x - (2 10^3 s ⁻¹)t] .

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