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MHT CET202521 Apr 2025Evening ShiftPhysicsWaves and SoundActual

The equation of a progressive wave is Y=3 [ ( t 3 - x 5 )+ 4 ] where x and y are in meter and time in second. Which of the following is correct?

Options

  1. AWavelength =10 ~m
  2. BVelocity =1.5 ~m / s
  3. CAmplitude =3 ~cm
  4. DFrequency =0.2 ~Hz

Correct answer

A. Wavelength =10 ~m

Step-by-step solution

The wave equation is given as Y = 3 [ ( t 3 - x 5 ) + 4 ] , which simplifies to Y = 3 ( t 3 - x 5 + 4 ) . Comparing with the standard form Y = A ( t - kx + ) , the amplitude is A = 3 m, angular frequency = 3 rad/s, and wave number k = 5 rad/m. The wavelength is given by = 2 k = 2 /5 = 10 m, matching option A. The wave velocity is v = k = /3 /5 = 5 3 1.67 m/s, not 1.5 m/s as in option B. The frequency is f = 2 = 1 6 0.167 Hz, not 0.2 Hz as in option D. The correct choice is A .

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