《Electromagnetism, principles and application》教学课件（PPT讲稿）Chapter 20 Electromagnetic Waves

The quantity v is called the phase velocity of the wave, since it is the velocity with which the wave front propagates in space For instance, in 1-dimensional case, take C= 0 The wave front is given by that is at times t the position of the front is at z=ut The wave length is the distance travelled over a pe riod T=1/f 入=0T=/f=0/(/2x)=27/u

a plane wave can be also written as a complex func- tion In the 1-dim case a=a0el(a(t-2/)-=a0ect+-272/) ao cow(t-2/u)+iao sinw(t-2/v) a0 COS(ut-2x/入)+isin(ut-2丌2/入)

20.2 The Wave Equation We take the 2nd derivative of a- goei(w(t-2/v) w.r.t. the time t We take the 2nd derivative of a= coei(w(t-2/u) w.r.t. the coordinate 2. 02a(2) From these two equations we get 02a(2m)2a2a1a2 a22a2入2at2 O This is the partial differential equation of waves in 1-dim case

In 3-dimensional case the plane wave equation is 1 a2c V-a at a general wave is a more complicated than this one

2rU Figure 20-2 The quantity a= o cos o[t-(z/u) as a function of z and as a function of t