JEE Main & Advanced Physics Wave Mechanics Question Bank Progressive Waves

  • question_answer
    A transverse sinusoidal wave of amplitude a, wavelength l and frequency n is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If \[a={{10}^{-3}}\,m\] and \[v=10\,m{{s}^{-1}}\], then l and n are given by     [IIT 1998]

    A)            \[\lambda =2\pi \times {{10}^{-2}}\,m\]                      

    B)            \[\lambda ={{10}^{-3}}\,m\]

    C)            \[n=\frac{{{10}^{3}}}{2\pi }Hz\]                                       

    D)            \[n={{10}^{4}}\,Hz\]

    Correct Answer: A

    Solution :

     \[{{v}_{\max }}=a\omega =\frac{v}{10}=\frac{10}{10}=\]m/sec \[\Rightarrow \]\[a\omega =a\times 2\pi n=1\]\[\Rightarrow \]\[n=\frac{{{10}^{3}}}{2\pi }\]      \[(\because \,\,a={{10}^{-3}}\,m)\]                    Since \[v=n\lambda \Rightarrow \lambda =\frac{v}{n}=\frac{10}{{{10}^{3}}/2\pi }=2\pi \times {{10}^{-2}}\]\[m\]


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