Obtain the equation of frequency of oscillations in string tied at both ends.

Explanation

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.