JEE Main & Advanced Physics Wave Mechanics Question Bank Progressive Waves

  • question_answer
    A wave equation which gives the displacement along the Y direction is given by the equation \[y={{10}^{4}}\sin (60t+2x)\], where x and y are in metres and t is time in seconds. This represents a wave [MNR 1983; IIT 1982; RPMT 1998; MP PET 2001]

    A)            Travelling with a velocity of 30 m/sec in the negative X direction

    B)            Of wavelength p metre

    C)            Of frequency 30/p Hz

    D)            Of amplitude \[{{10}^{4}}\]metre travelling along the negative X direction

    Correct Answer: A

    Solution :

     On comparing the given equation with \[y=a\sin (\omega \,t+kx),\] it is clear that wave is travelling in negative x-direction. It's amplitude a = 104 m and w = 60, k = 2. Hence frequency \[n=\frac{\omega }{2\pi }=\frac{60}{2\pi }=\frac{30}{\pi }Hz\] \[k=\frac{2\pi }{\lambda }=2\] Þ \[\lambda =\pi \,m\] and \[v=\frac{\omega }{k}=\frac{60}{2}=30\,m/s\]


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