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Obtain the equation of frequency of oscillations in string tied at both ends. |
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Answer» Solution :Let a string of length L is tied at two ends and it has tension. Its one end is tied at x=0 and another at x=L. For node, displacement sin kL =0 at any point. (Here x =L) `therefore kL = n pi` (where `n = 1,2,3,…,n)` `therefore (2pi L)/(LAMDA ) = n pi ` `therefore L = (n lamda)/(2)""...(1) ` where `n = 1,2,3,...,` `therefore lamda = (2L )/(n) ""...(2) n =1,2,3,...` and `v = lamda v` where v is speed of wave and v is frequency. `therefore (u)/(v) = lamda = (2L)/(n)` `therefore v = (nv)/(2L)""...(3) n = 1,2,3,...,` Equation (2) is for wavelength of stationary wave and equation (3) is for its natural frequency. |
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