A Complex Wave in One Dimension

This Demonstration shows complex waves of varying shape, amplitude, frequency, phase velocity, and group velocity, moving in one dimension.

Details

This Demonstration shows the complex wave

ψ(x,t)

that is the sum of five waves

i(

k

i

x-

w

i

t)

e

,

i=1,…,5

:

ψ(x,t)=

i(

k

1

x-

w

1

t)

e

+

i(

k

2

x-

w

2

t)

e

+

i(

k

3

x-

w

3

t)

e

+

i(

k

4

x-

w

4

t)

e

+

i(

k

5

x-

w

5

t)

e

.

The real and imaginary parts of

ψ

are plotted against

x

:

(x,Re(ψ),Im(ψ))

.

The phase velocity is given for waves 1 (

v

ϕ

=

w

1

k

1

) and 5 (

v

ϕ

=

w

5

k

5

).

The group velocity is approximated by

v

g

=

w

5

-

w

1

k

5

-

k

1

and is only valid with "beat" or "wave packet" selected.

Permanent Citation

Cedric Voisin

"A Complex Wave in One Dimension"
http://demonstrations.wolfram.com/AComplexWaveInOneDimension/
Wolfram Demonstrations Project
Published: October 7, 2024