How to model a transverse wave in Matlab (Wave Equation)
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if true
% USE POTENTIAL SOLUTION TO SCALAR WAVE EQUATION TO
% PLOT S WAVE
clear
% TIME DOMAIN
t = 0:1:500;
% WAVE VECTOR
k1 = 0.4;
k2 = 0.2;
k3 = 0.3;
% COORDINATES OF RAY (DETERMINED BY WAVE VECTOR)
x = 0:2.5:50;
y = k2/k1*x;
z = k3/k1*x;
% DIV(K,X)
KX = sum([k1*x; k2*y; k3*z]); % k.x
% OTHER WAVE PARAMETERS
A = 3; % AMPLITUDE
w = 0.1; % ANGULAR FREQUENCY
% LOOP OVER TIME STEPS
for n = 1:numel(t)
% DISPLACEMENTS (CURL OF SCALAR POTENTIAL):
ux = k1*A*(sin(w*t(n) - KX));
uy = k2*A*(sin(w*t(n) - KX));
uz = k3*A*(sin(w*t(n) - KX));
% PLOT WAVE FOR CURRENT TIME STEP
hold off
plot3(x,y,z,'r-');
hold on
plot3(x+ux,y+uy,z+uz,'ko','markersize',4,...
'markerfacecolor','k');
axis equal
axis([-10 55 -10 30 -5 40])
xlabel('x'), ylabel('y'), zlabel('z')
title(num2str(t(n)))
grid on
drawnow
end end
The current code models a longitudinal wave; a wave that oscillates along the direction of propagation.
However, I am trying to model a transverse wave, where the wave oscillates perpendicular to the direction of propagation.
u(z,t) = ∇φ(z,t) = (0,0,−ik)Aexp[i(ωt − kz)] is what dictates the longitudinal wave (z is direction of propagation)
here A (which is amplitude, defined by A = 3 in the code, is just a variable)
u(z,t) = ∇ × Ψ(z,t) = (ikAy ,−ikAx ,0)exp[i(ωt − kz)] is what dictates the transverse wave. Here, A is a vector quantity, and I am not sure how to define my previously used variable A, and split it into Ax and Ay.
Thanks for any help
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