Question

2. Sketch the function cos[w(t-v) overwz/u for value at-0, π/4,π/2,3%,π. (one diagram for cach ot) Esplain how this can be regarded as a propagating wae Repeat this procedure for cos co e

Answer 1

Cos[w(t-z/v)]=cos(wt-wz/v)=cos(wt-X)

Where X=wz/v is a new variable used for simplicity.

Matlab code:

wt=input('enter value of wt');
x=0+wt:0.01:(6*pi)+wt;
E=cos(wt-x);
plot(x,E);
xlabel('x=wz/v');
ylabel('EM Wave');
title(sprintf('For wt= %f rad', wt));

Result:

11:24 Commands edit emwave >emwave enter value of wt >>emwave enter value of wt pi/4 >>emWave enter value of wt pi/2 >>emwave enter value of wt 3*pi/4 >>emwave enter value of wt pi

For wt= 0.000000 rad 0.8 0.6 F 0.4 0.2 0.2 0.4 0.6 0.8 -1 0 16 2 4 10 14 18 12 20

11:21 Show Data Cursor Figure 1: pi/4 For wt-0.785398 rad 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 18 20 16 14 12

Figure 1: pi/2 For wt-1.570796 rad 0.8 0.6 0.4 0.2 0.2 -0.2 -0.4 0.6 -0.8 -1 10 15 20 25

Figure 1:3*pi/4 For wt: 2.356194 rad 0.8 0.6 0.4 0.2 0.2 -0.4 -0.6 0.8 22 20 -1 2 18 16 14 12 10 8 6 4

For wt:3.141593 rad 0.8 0.6 0.4 0.2 0.2 -0.4 0.6 0.8 -1 2 10 12 14 16 18 20 22

So we can see from above figures, the wave gets right shifted for increase in wt value i.e.the wave is travelling towards right side as time increases.

Replace the minus sign with '+' sign in above MATLAB CODE to get plots of cos[w(t+z/v)].