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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