Question

Can someone answer why x-vt describes a wave traveling to the right, and x+vt to the left? I UNDERSTAND THE MATHEMATICAL DERIVATION OF IT. Please don’t give me a long proof. It does not clarify anything.

x-vt is similar to adding a negative velocity, one with velocity going left, therefore the position would become more negative (more left), so why is this descriptive of something going to the right?

Example: if I’m +5m from the origin, and I am going right at +5m/s for 3s, I should end up at 20m from the origin. x-vt = (5m) - (5m/s)(3s) = -10m from origin. THIS is where mine, and I’m sure everyone else asking this question, confusion lies.

Answer 1

For simplicity set out coordinates so that x=0 when t=0. If the object is moving at a velocity v, then at any future time t, x=vt. So, x-vt = 0. That is, f(0) 'moves' along the positive x-axis with a velocity v.

If you can, plot the functions f(x)=cos (x-vt) , let v equal to any random number and plot it as you vary t between different graphs. You'll actually see the graph moving to the right as you increase t.I think it's a fantastically convincing argument for seeing how this works.