For stationary waves produced in a string of length I wavelength in the `n^(th)` mode is ......

Options

A. `(n ^(2))/(2l)`
B. `(t ^(2))/(2n)`
C. `(2l)/(n)`
D. `2ln`

Answer

C

Explanation

We have `y = 2a sin (kx) cos (omega t )`
At `x =l,` we always have `y=0` (nodal point)
`thereofre 0= 2a sin (kl) cos (omega t)`
`therefore sin (kl) =0`
But `sin (npi) =0` (Where `n = 1,2,3,…)`
`therefore kl = n pi`
`therefore (2pi)/(lamda)l = npi`
`therefore lamda = (2l)/(n) ` (Where `n ne 0 (n = 1,2,3,...)}`