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Punjab Medical Punjab - MET Solved Paper-2011

  • question_answer
    A string vibrates according to the equation \[y=5\sin \left( \frac{2\pi x}{3} \right)\cos 20\pi t\]where\[x\]and\[y\]are in cm and t in second. The distance between two adjacent nodes is

    A) \[3cm\]

    B) \[4.5cm\]

    C) \[6cm\]

    D) \[1.5cm\]

    Correct Answer: D

    Solution :

    \[y=5\sin \left( \frac{2\pi \,\,x}{3} \right)\cos 20\pi \,\,t\] Comparing with standard equation                 \[y=2\,\,A\sin \frac{2\pi x}{\lambda }\cdot \cos \frac{2\pi vt}{\lambda }\] \[\therefore \]  \[\frac{2\pi \,\,x}{\lambda }=\frac{2\pi \,\,x}{3}\] \[\Rightarrow \]               \[\lambda =3\,\,cm\] \[\therefore \]Distance between two adjacent nodes                 \[=\frac{\lambda }{2}=\frac{3}{2}=1.5\,\,cm\]


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