One can easily understand the result of the previous page
when one considers that all waves which are reflected
at the righthand side of the cord
have the same shape
as the incoming wave,
whereas all waves which are reflected
at the lefthand side of the cord
have the same shape
as the the first reflected wave.
So, we can restrict ourselves to the case of one wave moving
from the right to the left with speed v
interfering with one wave moving from the left to the right
with speed -v.
The displacement of a point at distance x
from the left end of the cord
at the instant t
is given by the sum of the displacements of each of the two waves
separately.
u(x,t) = uleft(x,t)
+ uright(x,t)
u(x,t) = A sin(k(vt-x)) + A sin(k(-vt-x))
u(x,t) = A sin(k(vt-x)) - A sin(k(vt+x))
u(x,t) = A sin(ωt-kx) - A sin(ωt+kx)
u(x,t) = - 2A sin(kx) cos(ωt)
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