JEE Main & Advanced Physics Wave Mechanics Question Bank Progressive Waves

  • question_answer
    The equation of a travelling wave is                    \[y=60\cos (1800t-6x)\] where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is                              [CBSE PMT 1997; JIPMER 2001, 02]

    A)            \[3.6\times {{10}^{-11}}\]      

    B)            \[3.6\times {{10}^{-6}}\]

    C)            \[3.6\times {{10}^{-4}}\] 

    D)            3.6

    Correct Answer: C

    Solution :

               Maximum particle velocity \[{{v}_{\max }}=\omega a\] and wave velocity \[v=\frac{\omega }{k}\]Þ \[\frac{{{v}_{\max }}}{v}=\frac{\omega a}{\omega /k}=ka\]. From the given equation\[k=\text{Co-efficient}\ \text{of}\,x=6micron\]\[\ =6\times {{10}^{-6}}m\] Þ \[\frac{{{v}_{\max }}}{v}=ka=6\times {{10}^{-6}}\times 60=3.6\times {{10}^{-4}}\]


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