Lecture 25 : Solution of Wave Equation in Homogeneous Unbound medium
Uniform Plane Wave
The time varying fields which can exist in an unbound, homogeneous medium, are constant in a plane containing
the field vectors and have wave motion perpendicular to the plane. This phenomenon is then called the `Uniform plane wave'.
Let us take an x-directed
- field which is constant in the xy-plane. The field therefore is given as
Substituting
in the wave equation and noting that
(since
is function of Z only)
we get
Note that since is a function of only, the partial derivative has been changed to full derivative. The propogation constant is defined as
The phase constant for the medium therefore is and the attenuation constant is zero.
The solution of the wave equation now is
The two terms on RHS represent the travelling waves moving in and directions respectively. Since in this case, is purely imaginary, (the attenuation constant for the medium is zero) , the two waves travel with constant amplitude and their amplitudes are and respectively anywhere in the space.
- field which is constant in the xy-plane. The field therefore is given as 
in the wave equation and noting that
is function of Z only) 
is defined as 
