PHYS 4D
Solution to HW 9
March 6, 2011
Problem Giancoli 36-64
(II) A certain galaxy has a Doppler shift given by
f
0
−
f
= 0
.
697
f
0
, How fast is it
moving away from us?
Solution:
f
0
−
f
= 0
.
697
f
0
⇒
f
f
0
= 0
.
303
.
The galaxy is moving away from the Earth. Eq. 36-15b
⇒
f
=
f
0
√
c
−
v
c
+
v
⇒
v
=
1
−
f
2
f
2
0
1 +
f
2
f
2
0
c
= 0
.
83
c.
Problem Giancoli 36-66
(II) Starting from Eq. 36-15a, show that the Doppler shift in wavelength is
∆
λ
λ
=
v
c
if
v
≪
c
.
Solution:
Eq. 36-15a:
λ
=
λ
0
√
c
+
v
c
−
v
λ
−
λ
0
λ
=
1
−
√
c
−
v
c
+
v
= 1
−
√
1
−
v
c
1 +
v
c
= 1
−
(
1
−
v
c
)
1
2
(
1 +
v
c
)
−
1
2
≈
1
−
(
1
−
v
c
)
=
v
c
.
Problem Giancoli 36-68
(III) A certain atom emits light of frequency
f
0
when at rest.
A monatomic gas
composed of these atoms is at temperature
T
. Some of the gas atoms move toward and others away from an observer
due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference

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