2. Solved Papers
  3. Manipal Engineering

Manipal Engineering Manipal Engineering Solved Paper-2015

  • question_answer
    A sinusoidal wave travelling in the positive direction on stretched string has amplitude 20 cm, wavelength 1 m and wave velocity 5 m/s. At x = 0 and t = 0, it is given that y = 0 and \[\tan \left( {{\sec }^{-1}}x \right)=\sin \left( {{\cos }^{-1}}\frac{1}{\sqrt{5}} \right),\]Find the wave function y (x,t).

    A) \[\pm \frac{3}{\sqrt{5}}\]

    B) \[\pm \frac{\sqrt{5}}{3}\]

    C) \[\pm \sqrt{\frac{3}{5}}\]

    D) \[y=(2x-1){{e}^{2(1-x)}}\]

    Correct Answer: C

    Solution :

     We start a general form for a rightward moving wave,\[\frac{x}{-2}+\frac{y}{1}=1\]...(i) The given amplitude is A = 2 cm = 0.02 m The wavelength is given as\[\frac{x}{2}-\frac{y}{3}=-1\] Wave number \[\frac{x}{-2}+\frac{y}{1}=-1\] Angular frequency,\[\frac{x}{2}+\frac{y}{3}=1\] From Eq. (i),\[\frac{x}{2}+\frac{y}{1}=1\] \[({{a}^{2}},-{{b}^{2}})\]For x = 0, t = 0 y = 0 and \[{{x}^{2}}+9<{{(x+3)}^{2}}<8x+25,\] i.e.      \[\frac{x+y}{x-y}=\frac{5}{2},\]                     (as y = 0) and   \[\frac{x}{y}\] From these conditions, we may conclude that \[\frac{3}{8}\] where n = 0, 2, 4, 6,... Therefore, \[\frac{8}{3}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner