PHYS 342 - Lecture 2 Notes - F12

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 1/14

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. 

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 2/14

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

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 3/14

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 

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 4/14

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

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 5/14

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

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 6/14

Lecture 2

Interference

vc’  c’ 

c+v

c-v

constructive

destructive

2)2(   A I  !

0= I 

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 7/14

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.

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 8/14

Lecture 2

Michaelson-Morley Experiement

Schematics:

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 9/14

Lecture 2

Experiment Setup

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 10/14

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   !

+!

"!=#

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 11/14

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   !

+

!

"#!#=$#

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 12/14

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!

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 13/14

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   !=

The image cannot be displayed.Your computer may not haveenough memory to open theimage, or the image may have beencorrupted. Restart your computer,and then open the file again. If thered x still appears, you may have to

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

8/11/2019 PHYS 342 - Lecture 2 Notes - F12

http://slidepdf.com/reader/full/phys-342-lecture-2-notes-f12 14/14

Lecture 2

Reading Assignments

•  Chapter 1, 1-2, 1-3