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Wave Equation
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Progressive Plane Wave
s
=
s
o
sin
[
2
π
(
t
T
±
x
λ
)
+
α
]
s=s_o \sin [2\pi (\frac{t}{T} \pm \frac{x}{\lambda}) + \alpha ]
s
=
s
o
sin
[
2
π
(
T
t
±
λ
x
)
+
α
]
Standing Wave Equation
s
=
A
cos
(
2
π
x
λ
+
ϕ
2
)
sin
(
2
π
t
T
+
ϕ
2
)
s=A\cos \left(2\pi \frac{x}{\lambda}+\frac{\phi}{2}\right) \sin \left(2\pi \frac{t}{T}+\frac{\phi}{2}\right)
s
=
A
cos
(
2
π
λ
x
+
2
ϕ
)
sin
(
2
π
T
t
+
2
ϕ
)
where
ϕ
\phi
ϕ
is the phase shift at origo. Node distance is
λ
2
\frac{\lambda}{2}
2
λ
The General Wave Equation
∂
2
s
∂
t
2
=
v
2
∂
2
s
∂
x
2
\frac{\partial^2 s}{\partial t^2}=v^2 \frac{\partial^2 s}{\partial x^2}
∂
t
2
∂
2
s
=
v
2
∂
x
2
∂
2
s
Occilation Frequency
f
occilation
=
∣
f
1
−
f
2
∣
f_{\textup{occilation}} = |f_1-f_2|
f
occilation
=
∣
f
1
−
f
2
∣