Give difinition, equation and unit for waveength and wave number for wave.

Explanation

Wavelength: The linear distance between any two points or particles having phase difference of `2pi` rad is called the wavelength (1) of the wave. Its SI unit is meter (m).
OR
The distance between consecutive crests/though is called a wavelength oof a wave.
`y (x,0) =a sin kx " "[because t =0 implies phi =0]`
From this equation, sin function repeats its value after interval of `2pi` phae difference solution of function,
`therefore sin kx = sin (kx + 2n pi)=sin [ K(x + (2n pi)/(k)) ]`
It means displacement at point x and x` + (2n pi)/(k)` are equa where, `n = 1,2,3,..`
For minimum displacement between two points of same displacement, n =1 have to be taken,
`therefore x + (2pi)/(k) -x=` wavelength
`therefore (2pi)/(k) =` wavelength` lamda`
`or k = (2pi)/(lamda)`
where k is called anguar wave no. or wave vector.
Unit of k is raisn `"meter"^(-1)` but as rad is unitless, its SI unit is `m^(-1)`
Its dimensional formuls is `[ M^(0) L^(-1) T ^(0)].`