What is harmonic of oscilation (mode)? Give explanation of different harmonic (modes).

Explanation

"The system of oscillations with natural frequency is called normal mode. "
The possible minimum natural frequency is called fundamental mode of first harmonic.
Frequency for two ends of tensed string of stationary wave,
`v = (nv)/(2L)" "...(1)`
By substituing `v = (v)/(lamda)`
`L = (nv lamda )/(2v) = (n lamda )/(2)" "...(2)`
and `lamda = (2L)/(n )" "...(3)` where `n = 1,2,3,...`
If `n =1,` then
`v _(1) = (v )/(2L), L = (lamda _(1))/(2) and lamda _(1) = 2L` are obtained `v _(1)` is called fundamental or first harmonci.
If `n =2,` then
`v _(2) = (v)/(L) = 2v _(1), = lamda _(2) = lamda _(2) =L` are obtained `v _(2)` is called second harmonic.
If `n =3,` then
`v _(3) = (3v)/(2L) = 3v _(1), L = ( 3 lamda _(3))/(2) and lamda _(3) = (2)/(3)L`
are obtained `v _(3)` is called third harmonic. Thus, by keeping `n = 4,5,6...` fourth, fifth sixth harmonic are obtained respectively which are given as below.

In figure, A = Antinode and N = node.
Different harmonics can be represented by `v _(n) = nv _(1).`
It is not necessary that string will oscillate by any one of the frequencies only.
In general, string oscillates due to superposition of different modes. Among them some are strongly and some are weakly excited.
Musical instruments like sitar and violin are designed on this principle.
According to the principle of superposition, a stretched string tied at both end can vibrate simultaneously in more than one modes. Which mode is strongly excited depends on where the string is plucked or bowed.