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JEE MainPhysicsWaves and Sound

A transverse wave pulse on a string is described by the equation y(x,t) = 10 (2x + 8t)^2 + 5 where x and y are in metres and t is in seconds. The magnitude and direction of the velocity of the wave are:

Options

  1. A0.25 m s ⁻¹ along the positive x -direction
  2. B4 m s ⁻¹ along the positive x -direction
  3. C4 m s ⁻¹ along the negative x -direction
  4. D0.25 m s ⁻¹ along the negative x -direction

Correct answer

C. 4 m s ⁻¹ along the negative x -direction

Step-by-step solution

The general form of a travelling wave is y = f(kx t) . For the given wave pulse, the phase argument is (2x + 8t) . Comparing this with (kx + t) , we get k = 2 m ⁻¹ and = 8 rad s ⁻¹ . The wave velocity is given by v = k = 8 2 = 4 m s ⁻¹ . Since the sign between the spatial ( x ) and temporal ( t ) terms is positive, the wave is travelling in the negative x -direction. Answer: 4 m s ⁻¹ along the negative x -direction

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