% twowaves; % Some elementary wave exercises to demonstrate the % effects of superposition, interferance, etc., between % two sinusoidal waves by way of a Matlab movie. % % Jim Price, January, 2000 clear clear memory close all % Set some default graphics things. set(0,'DefaultTextFontSize',14) set(0,'DefaultAxesFontSize',14) set(0,'DefaultAxesLineWidth',1.4) set(0,'DefaultLineLineWidth',1.6) str2(1) = {'twowaves:' }; str2(2) = {' '}; str2(3) = {'Demonstrate the superposition of two sinusoidal '}; str2(4) = {'propagating waves (red and green). The red wave has'}; str2(5) = {'frequency and wavenumber set to (5, 5). Choose the'}; str2(6) = {'frequency and wavenumber of the green wave by '}; str2(7) = {'clicking the mouse anywhere on the dispersion diagram.'}; str2(8) = {'The superposition of the waves is solid blue, and '}; str2(9) = {'their envelope is dashed blue. The phase speeds '}; str2(10) = {'of the base waves are evident by the motion of '}; str2(11) = {'red and green asterisks; the blue asterisk is the '}; str2(12) = {'carrier (or average). Note that the envelope, or group,'}; str2(13) = {'moves at the speed of the moving group speed.'}; str2(14) = {' '}; str2(15) = {' **** Hit any key to continue. **** '}; str2(17) = {''}; str2(18) = {'Jim Price, January, 2001 and 2010.'}; hf3 = figure(10); clf set(hf3,'Position',[50 50 600 500]) set(gca,'Visible','off') text(0, 0.50, str2,'FontSize', 12, 'HorizontalAlignment', 'left') pause figure(1) clf reset orient tall x = -15:0.05:15; % the distance domain dt = 0.1; % the time step nstep = 200; % number of time steps to take M = moviein(nstep); % define the wavelengths and wavenumbers of two pure waves % the base wave (the second pair is selected with the mouse) k1 = 5.; omega1 = 5.; % plot the dispersion diagram subplot(2,1,1) plot(k1, omega1, 'r*') hold on; plot([0 10], [0 10], ':b') axis([4 6 4 6]) axis('square') grid xlabel('wavenumber, k') ylabel('frequency, \omega') title('choose the dispersion relation') aaa = ... ' Use the mouse to select the (k, \omega) of the second, green wave.' [k2, omega2] = ginput(1) hold on plot(k2, omega2, 'g*') c1 = omega1/k1; c2 = omega2/k2; cgc = (omega2 + omega1)/(k2 + k1); cg = (omega2 - omega1)/(k2 - k1); deltg = 10; if cg <= 0; deltg = -10.; end for j = 1:nstep t = j*dt; arg1 = k1*x - omega1*t; arg2 = k2*x - omega2*t; s1 = cos(arg1); s2 = cos(arg2); sum = s1 + s2; sg = 2*cos((k2-k1)*x/2 - (omega2 - omega1)*t/2); subplot(2,1,2) plot(x, sum, 'b', 'linewidth', 1.5) hold on plot(x, s1, 'r', x, s2, 'g') plot(x, -sg, '--b', 'linewidth', 1.5) plot(x, sg, '--b', 'linewidth', 1.5); plot(t*c1-10, 0, '*r', t*c2-10, 0, '*g', t*cgc-10, 0, '*b') hp = text(t*cg-deltg, 0, 'group', 'color', 'b'); hold off xlabel('x distance') ylabel('amplitude') axis([-15 15 -2 2]); M(:,j) = getframe; end % rerun the movie movie(M,2,6);