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MHT CET202619 April 2026Evening ShiftPhysicsWaves and SoundActual

The equation of a progressive wave is given by y = 6 (100t - 4x) where y is in m , x in metre and t in second. The ratio of the maximum particle velocity to the velocity of wave is

Options

  1. A1.5 10⁻⁵
  2. B2.0 10⁻⁶
  3. C2.4 10⁻⁵
  4. D2.8 10⁻⁶

Correct answer

C. 2.4 10⁻⁵

Step-by-step solution

The given equation of the progressive wave is y = 6 (100t - 4x) . Comparing this with the standard wave equation y = A ( t - kx) , we get: Amplitude A = 6 m = 6 10⁻⁶ m Angular frequency = 100 rad/s Wave number k = 4 m ⁻¹ The maximum particle velocity is given by v_ p, max = A . The velocity of the wave is given by v_w = k . The ratio of the maximum particle velocity to the wave velocity is: v_ p, max v_w = A k = Ak Substituting the values of A and k : Ratio = (6 10⁻⁶) 4 = 24 10⁻⁶ = 2.4 10⁻⁵ Answer: 2.4 10⁻⁵

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