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Give difinition, equation and unit for waveength and wave number for wave. |
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Answer» Solution :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)].` |
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