A clamped string is oscillating in `n^(th)` harmonic, then :-

Options

A. Total energy of oscilations will be `n^(2)` times that of fundamental frequency
B. Total energy of oscillations will be `(n-1)^(2)` times that of fundamental frequency
C. Average kinetic energy of the string over a complete oscillations is half of that the total energy of the string
D. None of these

Answer

A, C

Explanation

Total energy
`=(1)/(2)muomega^(2)A^(2)=2pi^(2)f_(n)^(2)muA^(2)=2pi^(2)n^(2)f_(1)^(2)muA^(2)`
(`f_(1)` = fundamental frequency
`f_(n)` = Frequency of `n^(th)` harmonic
`lt KEgt = lt PEgt =(TE)/(2)`