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JEE Main & Advanced Physics Wave Mechanics Question Bank Vibration of String

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    A string is producing transverse vibration whose equation is \[y=0.021\ \sin (x+30t)\], Where x and y are in meters and \[t\] is in seconds. If the linear density of the string is \[1.3\times {{10}^{-4}}\]kg/m, then the tension in the string in \[N\] will be [RPET 1999; RPMT 2002]

    A)            10  

    B)            0.5

    C)            1    

    D)            0.117

    Correct Answer: D

    Solution :

                         \[y=0.021\sin (x+30t)\]Þ \[v=\frac{\omega }{k}=\frac{30}{1}=30\,m/s\].                    Using, \[v=\sqrt{\frac{T}{m}}\Rightarrow 30=\sqrt{\frac{T}{1.3\times {{10}^{-4}}}}\Rightarrow T=0.117\]N


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