The electric field of an electromagnetic wave is given by
`E_(y)=30cos(2pixx10^(8)t-(2pi)/(3)x)`
where, E is in volt/metre, t in second and x in metre. Determine.
(a) The wavelength
(b) (b) Direction of propagation of the wave
(c) Frequency

Explanation

Given,
The electric field of an electromagnetic wave,
`E_(y)=30cos(2pixx10^(8)t-(2pi)/(3)x)`
or `E_(y)==30cos((2pi)/(3)x-2pixx10^(8)t)" "......(i)`
Comparing with standard equation,
`E_(y)=E_(0)(0)(kx-omegat)`
The wavelngth, `lamda=(2pi)/(k)`
`=(2pi)/(((2pi)/(3)))=3m" "( :.k=(2pi)/(3))`
(b) Electromagnetic wave propagates along x-direction.
(c ) Angular frequency, `omega=2pixx10^(8)`
or, `2piv=2pixx10^(8)`
Frequency, `v=10^(8)` Hz