Homework 1
Physics 2130
Modern Physics
Due: Wednesday September 4, 2002
1. Taylor and Zaratos, problem 1.8.
ABC
D
v
u
u
u
A
D
C
Figure 1: Geometry for problem #1.
We're given that the wind speed
v
= 30 m/s and that sound propagates in the air with a sp eed
of
u
= 330 m/s:
u
A
=
u
,
v
= 300 m/s (1)
u
B
=
u
+
v
= 360 m/s (2)
u
D
=
p
u
2
,
v
2
=328
:
6m/s (3)
2. Taylor and Zaratos:
Exploration of the binomial approximation: (1
,
x
)
n
1
,
nx
for
j
x
j
<<
1.
(a) Problem 1.10.
x
(1
,
x
)
,
1
=
2
1+
x=
2 % dierence
0.001 1.0005004 1.0005000 0.00004%
0.01 1.00504 1.00500 0.004%
0.1 1.054 1.050 0.4%
0.5 1.414 1.250 12%
(b) Problem 1.12.
Using the binomial approximation: (1
,
10
,
20
)
,
1
,
1
1+10
,
20
,
1=
10
,
20
.
3. Taylor and Zaratos, problem 1.15.
The expected fringe shift is (eqn. 1.10 of T&Z):
N
=
2
`
2
=2
0
:
5
m
590
10
,
9
m
3
10
4
m=s
3
10
8
m=s
!
2
=0
:
017 radians
;
(4)
where
=
v=c
. This is about 1/60 of a complete fringe. The negative result of not observing this
small fringe shift was not taken seriously. Michelson and Morley later lengthened the arms of the
interferometer by a factor of about 20 to 11 m, however, and increased this value to about 1/3 of a
complete fringe which was easily observable.
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