Give definition, SI unit and dimensional formula of time period, angular frequency and frequency of wave.

Explanation

Time period: "The time taken by any string element to move through one complete oscillation is called Time period (T)".
In equation of displacement of wave,
`y (x,t)=a sin (kx - omega t + phi) if phi =0,` then if we observed motion of element at `x=0.`
`y(0,t) =a sin (-omega)` `y (0,t)=- a sin omega t ` which is shown in below figures. The element moves up and down in SHM with amplitude a and time period T.

`therefore - a sin omega t =- a sin [omega (t +T)]`
`=- a sin (omega t + omega T)`
but as since function is repeating at `2pi` interval, `omega T=2pi`
`therefore omega = (2pi)/(T)`
where `omega` is called angular frequency of wave.
Angular frequency of oscillations of frequency of wave.
Its symbol is `omega ` and SI unit is `rad s ^(-1)` and dimensional formula is `[M^(0) L ^(0) T ^(-1)].`
Frequency : The number of oscillations performed by the particle of medium in one second is know as the frequency of oscillation of particle. Its symbol is .v. of .f. Sometime it is also written as `eta.`
If 1 wave is obtained in T time, then in 1 sec . (f) waves re obtained,
`v or f = 1/T = (omega)/(2pi)`
`therefore` SI unit of frequency is `s ^(-1) or .Hz.` and its dimensionalformula is `[M^(0) L ^(0) T ^(-1)].`