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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    \[y=3\sin \,\pi \left( \frac{t}{2}-\frac{x}{4} \right)\] represents an equation of a progressive wave, where t is in second and \[x\] is in metre. The distance travelled by the wave in 5 s is

    A)  8 m                                       

    B)  10 m

    C)  5 m                                       

    D)  32 m

    Correct Answer: B

    Solution :

    The given equation of a progressive wave is \[y=3\sin \pi \left( \frac{t}{2}-\frac{x}{4} \right)=3\sin \,2\pi \left( \frac{t}{4}-\frac{x}{8} \right)\] The standard equation of a progressive wave is                 \[y={{y}_{0}}\sin 2\pi \left( \frac{t}{T}-\frac{x}{\lambda } \right)\] Comparing these two equations, we get                 \[T=4\,\,s,\,\,\lambda =8\,\,m\] \[\therefore \] Velocity of wave,                 \[v=\frac{\lambda }{T}=\frac{8}{4}=2\,m{{s}^{-1}}\] Distance travelled by wave in time t is                 \[s=vt\] or            \[s=2\times 5=10\,m\]


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