PHYS 342 - Lecture 2 Notes - F12

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.



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



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



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



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



Lecture 2

Interference

vc’ c’

c+v

c-v

constructive

destructive

2)2( A I !

0= I



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.



Lecture 2

Michaelson-Morley Experiement

Schematics:



Lecture 2

Experiment Setup



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 !

+!

"!=#



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 !

+

!

"#!#=$#



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!



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



Lecture 2

Reading Assignments

• Chapter 1, 1-2, 1-3

Documents

PHYS 342 - Lecture 2 Notes - F12