# The Wave Function of a Wave Equation Shifted

Posted by doug
summary:
A phase shift is added to a wave function, but you cannot tell due to the periodic boundary condition.
description:
A change in the phase was included. Each event above another event has a different starting time due to the phase shift, but given enough time, all the same locations in spacetime are experienced, so the pattern looks the same.
command:
q_graph -out amp_shifted -dir int14 -box 1.6 -command 't_function -t_func cos -x_func sin -y_func zero -z_func zero -n_steps 1000 -pi 10 -n_t_cycles 1000 -n_t_step 0.0314 1 1 0 0 | q_add 0 0 -1.5 0 | q_add_n_m 0 0 0.003 0 1000 1000' -color yellow
equation:

$\phi = (cos(\omega t + \delta), sin(\omega t + \delta), k \delta, 0) \, \textrm{with} \, \delta: 0 \to 10 \pi$