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Physics
Compare Relativistic and Nonrelativistic Doppler Shift Formulas
Example Notebook
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Find the full names of formulas for the Doppler shift in frequency:
I
n
[
1
]
:
=
F
o
r
m
u
l
a
L
o
o
k
u
p
[
"
d
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p
l
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r
s
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f
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q
u
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n
c
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"
]
/
/
T
a
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F
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O
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[
1
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/
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T
a
b
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=
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c
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D
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p
p
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f
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F
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q
u
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c
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O
b
s
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r
v
e
r
S
p
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d
D
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q
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c
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W
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p
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d
W
i
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d
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d
D
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p
p
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a
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v
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s
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q
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c
y
D
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p
p
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r
S
h
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f
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v
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F
r
e
q
u
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n
c
y
O
b
s
e
r
v
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r
S
p
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d
Get a specific equation:
I
n
[
2
]
:
=
F
o
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m
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a
D
a
t
a
[
{
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,
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y
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}
]
O
u
t
[
2
]
=
f
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f
s
c
c
+
v
s
I
n
[
3
]
:
=
F
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m
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{
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}
]
O
u
t
[
3
]
=
f
o
f
s
c
-
v
s
c
+
v
s
Define functions that solve for specific quantity variables:
I
n
[
4
]
:
=
d
o
p
p
l
e
r
[
v
_
]
:
=
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,
{
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[
4
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]
,
v
s
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,
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c
"
Q
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[
1
,
"
S
p
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d
O
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]
}
]
I
n
[
5
]
:
=
d
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p
p
l
e
r
r
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l
a
t
i
v
i
s
t
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c
[
v
_
]
:
=
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q
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,
{
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[
4
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,
"
M
e
g
a
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r
t
z
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]
,
v
s
v
}
]
Compare relativistic and nonrelativistic formulas in a plot:
I
n
[
6
]
:
=
P
l
o
t
{
d
o
p
p
l
e
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[
Q
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n
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i
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,
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d
O
f
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]
]
,
d
o
p
p
l
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e
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a
t
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v
i
s
t
i
c
[
Q
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t
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[
v
,
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p
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L
i
g
h
t
"
]
]
}
,
{
v
,
0
,
0
.
9
}
,
O
u
t
[
6
]
=
r
e
l
a
t
i
v
i
s
t
i
c
n
o
n
r
e
l
a
t
i
v
i
s
t
i
c
Use
S
e
r
i
e
s
to compare the two formulas symbolically for low speeds to expose how they differ in the factor of the (v/c)^2 term:
I
n
[
7
]
:
=
S
e
r
i
e
s
c
-
v
s
c
+
v
s
,
{
v
s
,
0
,
2
}
O
u
t
[
7
]
=
1
+
-
1
/
c
v
s
+
1
2
/
2
c
2
v
s
+
3
O
[
v
s
]
I
n
[
8
]
:
=
S
e
r
i
e
s
c
c
+
v
s
,
{
v
s
,
0
,
2
}
O
u
t
[
8
]
=
1
-
v
s
c
+
2
v
s
2
c
+
3
O
[
v
s
]
Related Symbols
FormulaLookup
FormulaData
Quantity
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