Problem 20-35; combining standing waves is a very important problem.
Contrary to the feedback I was getting, this is not a messy problem.
It has very important conceptual content relevant to understanding
both waves on a string and particle/wave time dependence in quantum mechanics.
To start with you must realize that f2=2f1, and that, of course, f1 is in the denominator (the bulletin board comments
addressed this.
At t=0 you do have to add together 2 waves to get a plot
t=0 and 1/(8f1) plots , but for each of the next three times one of the normal
modes is zero at all x. At the last time (t=4/(8f1) is almost exactly the same as the first, but with
the sign changed for one wave!
Click on this to see plots for problem 20-35 c):
Prob 20-35 ,
[is this right, or did I get the times mixed up? Please check this!]
Extra credit: Can Anyone calculate [x] as a function of time for the normal mode combination of
prblem 20-35? [x] is the integral of x times y(x,t)**2 (squared) (vs x from 0 to el) divided by
the integral of y(x,t)**2 (squared) (vs x from 0 to el)
, which is, physically, the average "position of the wave".
[Warm up problems: what is [x] for either normal mode by itself? What is [x] for y= A*exp{-(x-vt)**2} ?]
If this is as interesting as I hope, it could be worth beaucoup xtra crdit!