Wave PhysicsPHYS 2023

Tim Freegarde

14 Impedance2020-21

2

A frayed guitar string

2

1 0, txy

δx

2M

1M

3

Continuity conditions

• various derivations and forms

• typically: • one condition derived from balance of forces

• conservation of momentum

• the two conditions combined

• conservation of energy

• reduce to equations of the form

where are combinations of material properties

4

Impedance

5

Reflection at an interface

combine forward and reflected waves to give total

fields for each region

apply continuity conditions for separate components

hence derive fractional transmission and reflection

y

x

A B

6

Frayed guitar string

combine forward and reflected waves to give total

fields for each region

apply continuity conditions for separate components

hence derive fractional transmission and reflection

y

x

A B

• continuity conditions:

• parameters:

7

Electromagnetic waves at a normal interface

combine forward and reflected waves to give total

fields for each region

apply continuity conditions for separate components

hence derive fractional transmission and reflection

y

x

A B

• continuity conditions:

• parameters:

8

Continuity conditions

• for a boundary at between regions A and B:

• transverse waves on a string:

• electromagnetic waves:

non-normal incidence:

• sound waves:

• thermal waves:

9

Impedance

• sound waves:

• thermal waves:

• transverse waves on a string:

• electromagnetic waves:

• at interface between two media:

where

10

Impedance

• sound waves:

• thermal waves:

• transverse waves on a string:

• electromagnetic waves:

• at interface between two media:

11

Impedance choices

• There may be different ways to describe a wave disturbance

• the sign of the amplitude reflection coefficient depends upon the property described

• it may be difficult to identify the physical analogue to impedance (eg chemical waves)

system property alternative

string displacement gradient

electromagnetic electric field magnetic field

water horizontal displacement vertical displacement

sound displacement pressure

thermal temperature heat flow

• conventions may dictate a particular choice of definition

12

John N Shive (1913-1984)

• Bell Telephone Laboratories (AT&T)

https://www.youtube.com/watch?v=DovunOxlY1k

• wave demonstrator, based upontorsional waves

• illustrations of wave propagation, standing waves, impedance effects(1959)

13

John N Shive (1913-1984)

https://www.youtube.com/watch?v=DovunOxlY1k

Wolfgang Christian

• Bell Telephone Laboratories (AT&T)

• wave demonstrator, based upontorsional waves

• illustrations of wave propagation, standing waves, impedance effects(1959)

14

Phase change upon reflection

• phase change if

• for electromagnetic waves

in non-magnetic media

1515

Newton’s rings

diffuser

beam-splitter

lens

plates

r

• apply to sinusoidal waves by taking into account the phase with which components arrive

• combine by adding the amplitudes

• contributions may therefore interfere constructively or destructively

16

Reflection at non-normal incidence

17

Phase change upon reflection

• phase change if

• for electromagnetic waves

in non-magnetic media

1818

Brewster’s angle

www.paddling.net/sameboat/archives/sameboat496.html

i i

r

r

itan• reflected light fully (s-) polarized

Wave PhysicsPHYS 2023

Tim Freegarde