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JEE MainPhysicsWaves and Sound

A transverse harmonic wave on a string is given by y = y₀ (kx - t) . If the maximum particle velocity is equal to 4 times the wave velocity, then the wavelength of the wave is:

Options

  1. Ay₀ 4
  2. B8 y₀
  3. C2 y₀
  4. Dy₀ 2

Correct answer

D. y₀ 2

Step-by-step solution

The equation of the wave is y = y₀ (kx - t) . The maximum particle velocity is given by v_ p, max = y₀ . The wave velocity is given by v_w = k . According to the given condition, v_ p, max = 4 v_w . y₀ = 4 ( k ) y₀ = 4 k We know that the wave number k = 2 , where is the wavelength. y₀ = 4 ( 2 ) = 4 2 = 2 = y₀ 2 Answer: y₀ 2

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