There are two harmonic waves on a string:
y1=Aexp(i(kx-wt))
y2=Bexp(i(-kx-wt))
(1) y(x=0)=0
(2) y(=L) = 0
The total wave is
(3) y=exp(-iwt)[Aexp(ikx) + Bexp(-ikx)]
(1) gives A = -B, so that (3) can be written
y = exp(-iwt)[Aexp(ikL) - Aexp(-ikL)] = 0
For (2) to be true, we must have exp(ikL) - exp(-ikL) = 0, that is
cos(kL) + i sin(kL) - cos(-kL) - i sin (-kL) = 0 ---> 2sin(kL) = 0 ---> kL = n*pi
Is my book wrong when it says kL = 2n*pi?
y1=Aexp(i(kx-wt))
y2=Bexp(i(-kx-wt))
(1) y(x=0)=0
(2) y(=L) = 0
The total wave is
(3) y=exp(-iwt)[Aexp(ikx) + Bexp(-ikx)]
(1) gives A = -B, so that (3) can be written
y = exp(-iwt)[Aexp(ikL) - Aexp(-ikL)] = 0
For (2) to be true, we must have exp(ikL) - exp(-ikL) = 0, that is
cos(kL) + i sin(kL) - cos(-kL) - i sin (-kL) = 0 ---> 2sin(kL) = 0 ---> kL = n*pi
Is my book wrong when it says kL = 2n*pi?
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