This preview shows page 1. Sign up to view the full content.
PHY4604
R. D. Field
Department of Physics
Chapter1_4.doc
University of Florida
Re(
Ψ
)
A
Ψ
= Ae
i(kx
ω
t)
Im(
Ψ
)
φ
= kx
ω
t
t
Im(
Ψ
) = Asin(kx
ω
t)
A
A
Crest
Trough
A
Ψ
(0,t) = Ae
i
ω
t
Distance r
φ
= kr
ω
t
x = 0
φ
=
ω
t
A
x = r
Ψ
(r,t) = Ae
i(
kr

ω
t)
Representing Waves as Complex Numbers
We can use complex numbers to represent traveling waves.
If we let
)
(
t
kx
i
Ae
ω
−
=
Ψ
then
)
cos(
)
Re(
t
kx
A
−
=
Ψ
is a traveling plane wave with wave number
k = 2
π
/
λ
, “angular” frequency
ω
= 2
π
f
, and amplitude
A
.
The intensity,
I
, is proportional to
A
2
.
∗
ΨΨ
=
Ψ
=
A
2
2
Ψ
=
∝
A
I
PhaseShift Due to a Path Length Difference
Consider two traveling wave that are in phase at their source, but
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '07
 FIELDS
 mechanics

Click to edit the document details