phys 342 - lecture 2 notes - f12
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8/11/2019 PHYS 342 - Lecture 2 Notes - F12
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Lecture 2
Question
A loud speaker sits in a car that moves at a velocity v1.
What is the propagation speed of the sound waves from
the speaker as measured by an observer who runs toward it
at velocity v2? Assuming the speed of sound is c.
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Lecture 2
Failure of Newtonian Relativity
• Laws of electricity and magnetism (or Maxwell equations)
are not Galilean invariant
z x
y
dq
q
S
x’
y’
z ’
S ’
v
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Lecture 2
Failure of Newtonian Relativity-Cont
d
• The propagation speed of electromagnetic waves would,therefore, be affected by the motion of inertial frame ofreferences
Luminiferous ether: a hypothesized medium overwhich electromagnetic waves propagate
Existence of a preferred frame of
reference?
Unusual properties of ether: extremely rigid whileoffering no resistance to motion of the planets
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Lecture 2
Existence of Ether?
• Earth’s motion through ether
– Light travels at different speeds along differentdirections, as measured by an observer on the earth.
vc-v
c+v
LA B
! " #
$% &
++'
(
=
+
+
(=+= ))
!2
2
2
2 12
1
12
c
v
c
L
c
vc
L
vc
L
vc
Lt t t
A B B A
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Lecture 2
Existence of Ether – Cont d
v L
A
B
c’ c’
vccvvvoelole
!!!!!!
+!="+=
22222 vccvcc !="#+"=
$&
++'! #
$& (=
(=+=
(
))
!2
22/1
2
2
22
2
11
21
2
2
c
v
c
L
c
v
c
L
vc
L
t t t A B B A
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Lecture 2
Interference
vc’ c’
c+v
c-v
constructive
destructive
2)2( A I !
0= I
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Lecture 2
Coherence
!"#$
%& +'=
!"
#$%
&+'=
)(sin
)(sin
2
2
2
22
1
1
1
11
( )
( )
w
w
v
l t A s
v
l t A s
$&
'+'=(2
2
1
1
12
ww
v
l
v
l ) ) * +
Phase Difference:
!"
!#$
%&+=+&
%&='
edestructivnn
veconstructin
( ( (
(
) 2)
2
1(2
2
where
T
! "
2=
If 12 ! ! "
remains constant, the two waves are coherent.
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Lecture 2
Michaelson-Morley Experiement
Schematics:
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Lecture 2
Experiment Setup
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Lecture 2
Phase Difference Between Two Arms
$$&
++' !
2
2
11 1
2
c
v
c
Lt ! !
# $$&
++' !
2
2
22
2
11
2
c
v
c
Lt
8
2
2
2
10300000
30 !="
$ %'
=
c
vSince , we ignore higher order
terms and we have
c
L L
c
v
c
L Lt t
212
221
212)(2 !
+!
"!=#
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Lecture 2
Expected Shift in Fringe Pattern
Rotating the entire experiment setup by 90 degrees, we now have
The fringe pattern should, therefore, shift by
$$& '! ! # $$& +
'()*( 2
2
2
2
21 2
c
v L
c
v
cT
L L
T +
in terms of the fraction of the full width of a fringe.
c
L L
c
v
c
L L
t t
212
221
21
2)(2 !
+
!
"#!#=$#
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Lecture 2
Results
smc
smv
m
m L
8
4
7
103
103
109.5
11
!=
!=
!=
=
"#
Known quantities:
Expected shift:
40% of a fringe
But, the measured shift is <1%!
s
mv
3
105!<or
Modern measurements indicate s
mv 15<
Ether does not exist!
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Lecture 2
Lorentz-Fitzgerald Contraction
2
2
1
1
1
12
cvc
Lt
!
=
2
2
2
2
1
12
c
vc
Lt
!
=
We know
But, what if
2
2
1 1
c
v L L !=
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The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
We would then have
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Lecture 2
Reading Assignments
• Chapter 1, 1-2, 1-3