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JEE MainPhysicsWaves and Sound

A transverse wave travelling along the positive x-direction has an amplitude of 5 ~cm , a frequency of 50 ~Hz , and a wave speed of 20 ~m/s . Which of the following equations correctly represents this wave? (Assume x is in meters and t is in seconds)

Options

  1. Ay(x, t) = 5 (100 t + 5 x) ~cm
  2. By(x, t) = 5 (100 t - 5 x) ~cm
  3. Cy(x, t) = 5 (50 t - 20 x) ~cm
  4. Dy(x, t) = 5 (5 t - 100 x) ~cm

Correct answer

B. y(x, t) = 5 (100 t - 5 x) ~cm

Step-by-step solution

The angular frequency of the wave is: = 2 f = 2 50 = 100 ~rad/s The angular wave number is: k = v = 100 20 = 5 ~m ⁻¹ Since the wave is travelling in the positive x-direction, the kx and t terms in the phase must have opposite signs. The standard equation can be written as y(x,t) = A ( t - kx) or A (kx - t) . Substituting the calculated values and the given amplitude A = 5 ~cm , we get: y(x,t) = 5 (100 t - 5 x) ~cm Answer: y(x, t) = 5 (100 t - 5 x) ~cm

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