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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2001

  • question_answer
    Vibrations of rope tied by two rigid ends shown by equation \[y=\cos 2\pi t\,\sin \,2\pi t\] then minimum length of the rope will be:

    A)  1 m                                       

    B)  1/2 m

    C)  5 m                       

    D)         2n m

    Correct Answer: B

    Solution :

    Equation of vibration                  \[y=1\,\cos \,2\pi \,\sin \,2\pi x\]    \[=1\,\cos \,2\pi \,\sin \,\frac{\pi x}{1/2}\] Comparing this equation with        \[y=a\,\cos \,2\pi \,\sin \,\frac{\pi x}{\lambda }\Rightarrow a=1\] Minimum length of string \[=\frac{1}{2}a=\frac{1}{2}\times 1\] \[=\frac{1}{2}m\]


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