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NEETPhysicsWaves and Sound

The displacement of a string carrying a standing wave is given by y = A ( x L ) ( 2 t T ) , where x and y are in metres and t is in seconds. The speed of the two constituent progressive waves that interfere to produce this standing wave is:

Options

  1. AL 2T
  2. BL T
  3. CL T
  4. D2L T

Correct answer

D. 2L T

Step-by-step solution

The standard equation of a standing wave formed by two identical progressive waves travelling in opposite directions is y = 2A (kx) ( t) . Comparing the given equation y = A ( x L ) ( 2 t T ) with the standard form, we can identify the wave number and angular frequency of the constituent waves: Wave number, k = L Angular frequency, = 2 T The speed v of the constituent progressive waves is given by the ratio of angular frequency to wave number: v = k Substituting the identified values, we get: v = ( 2 T ) ( L ) = 2L

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