SLD
Contributor
Two people are holding a string 10 units long along the x axis. The person at point 0 moves the string up and down between 1 and -1 at a fixed rate. The person at the other end moves it left and right between 1 and -1 at the same rate. Describe the motion of the string in terms of x, y, z, and t.
If just one person was moving the string then there would be a sine wave traveling down the string and the solution is basically a partial differential equation that I learned in undergraduate days. I looked it up. Not too difficult. I figured if the string were suspended in a liquid and hit by transverse waves at the same frequency and along the axes described, it's a bit more difficult but doable.
But it’s the boundary problems here that are exceptionally difficult. The wave is pinched off at each end. At the origin the string only moves up and down and at the other end it only moves right and left. That constraint will affect the movement all along the axes.
Thoughts?
SLD
If just one person was moving the string then there would be a sine wave traveling down the string and the solution is basically a partial differential equation that I learned in undergraduate days. I looked it up. Not too difficult. I figured if the string were suspended in a liquid and hit by transverse waves at the same frequency and along the axes described, it's a bit more difficult but doable.
But it’s the boundary problems here that are exceptionally difficult. The wave is pinched off at each end. At the origin the string only moves up and down and at the other end it only moves right and left. That constraint will affect the movement all along the axes.
Thoughts?
SLD