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Prove that the equation y = a sin omegat...

Prove that the equation `y = a sin omegat` does not satisfy the wave equation and hence it does not represent a wave.

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To prove that the equation \( y = a \sin(\omega t) \) does not satisfy the wave equation, we will follow these steps: ### Step 1: Understand the Wave Equation The wave equation in one dimension is given by: \[ \frac{\partial^2 y}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 y}{\partial t^2} \] where \( v \) is the speed of the wave. ...
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Knowledge Check

  • Which of the following wave functions does not represent a travelling wave ?

    A
    `y=tan(x-vt)^(2)`
    B
    `y=log(x+vt)`
    C
    `y=1/(x+vt)`
    D
    All of these
  • Which of the following does not represent a travelling wave

    A
    `y = f (x-vt)`
    B
    `y = y_(m) sin k (x + v t )`
    C
    `y = y_(m) log (x-vt)`
    D
    `y = f(x^(2)-vt^(2))`
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