The electric field of an electromagnetic wave is given by `E_(y)=40sin((2pi)/(3)x-2pixx10^(8)t)`
where, E is in V/m, t is in second and x is in metre. Find (i) propagation vector k (ii) wavelength `lamda` and (iii) frequency of the electromagnetic wave.

Explanation

Here, Electromagnetic wave is given by
`E_(y)=40sin((2pi)/(3)x-2pixx10^(8)t)`
Comparing with standard equation
`E=E_(0)sin(kx-omegat)`
(i) Propagation vector `k=(2pi)/(3)m^(-1)`
`:.` As we know, propagation vector
`k=(2pi)/(lamda)implies(2pi)/(3)=(2pi)/(lamda)`
Wavelength `lamda=3` m
(iii) `:.` As, angular velocity
i.e., `omega=2pixx10^(8)rad//s`
`implies2piv=2pixx10^(8)`
Frequency of the electromagetic weve
`v=10^(8)Hz`