Electromagnetic Waves, Materials, and Computation with MATLAB®

89

7

Miscellaneous Topics on Waves

*

Most of the problems we have dealt with till now are monochromatic waves unbounded in

space. Practical signals involve pulse waves or beam waves. The simple solutions obtained

for monochromatic waves can be used to construct solutions for more difcult problems.

In this connection, we rst explore the concept of group velocity.

7.1 Group Velocity v

g

Group velocity is the velocity with which a group of waves travel. Let us consider that at

z = 0, we have two sinusoidal oscillations:

E t t t0, ) ) .

( )

= − + +sin( sin(

0 0

ω ω ω ωΔ Δ

(7.1)

The two oscillations differ in frequency by 2Δω.

Equation 7.1 may be also w