WOLFRAM|DEMONSTRATIONS PROJECT

Orthonormality of Standing Waves

integers

m

1

n

1

This Demonstration shows two standing waves and their inner product, checking the orthonormality condition

L

∫

0

f

m

(x)

f

n

(x)dx=

δ

m,n

. Each normalized wave has the form

f

k

(x)=

2

L

sin

kπx

L

(with

L=1

here).