KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    The wave-function for a certain standing wave on a string fixed at both ends is  \[y(x,\,\,t)=0.5\,\,\sin \,\,(0.025\,\pi x)\,\,\cos \,\,500t\] where x and y are in centimeters and t is in seconds. The shortest possible length of the string is -

    A) 126 cm

    B) 160 cm

    C) 40 cm

    D) 80 cm

    Correct Answer: C

    Solution :

    \[k=\frac{2\pi }{\lambda }=0.025\pi \] \[\Rightarrow \frac{\lambda }{2}=\frac{1}{0.025}=40\,\,cm.\] The shortest possible length will be \[{{L}_{\min }}=\frac{\lambda }{2}=40\,\,cm\]

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