Wave PhysicsPHYS 2023

Tim Freegarde

2

Wave propagation

use physics/mechanics to write partial differential

wave equation for system

insert generic trial form of solution

find parameter values for which trial form is a

solution

• transverse motion of taut string

• travelling wave:

• e-m waves along coaxial cable• shallow-water waves

• flexure waves• string with friction

• general form• sinusoidal• complex

exponential

• standing wave

• damped

• soliton

• speed of propagation• dispersion relation• string motion from initial conditions

3

Wave propagation in changing media

• Huygens’ construction

• gradual change: • refraction

• refraction; continuity conditions

• obstacles: • 1-D: boundary conditions

• 2/3-D: diffraction

• today’s lecture:

• interface between media:

4

Wave propagation

waves are• collective bulk disturbances, in

which• motion is a delayed response• to neighbouring motions

• the amplitudes are added

when propagation follows multiple routes

• waves propagate via all possible routes

5

Huygens’ wave construction

• wavefronts propagate from initial disturbance in all directions

Christiaan Huygens (1629-1695)

• each point on the wavefront acts as a secondary source

• further wavefronts propagate from the secondary sources in the same fashion

• where wavefronts coincide (strong constructive interference), a new wavefront is formed

6

Huygens’ wave construction

• two point sources

7

Huygens’ wave construction

• five point sources• two point sources

8

Huygens’ wave construction

• 21 point sources• five point sources

9

Huygens’ wave construction

• propagation from a point sourceChristiaan Huygens (1629-1695)

10

Huygens’ wave construction

• reflection at a plane surfaceChristiaan Huygens (1629-1695)

11

Huygens’ wave construction

• refraction at a plane surfaceChristiaan Huygens (1629-1695)

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Huygens’ wave construction

• refraction at a plane surfaceChristiaan Huygens (1629-1695)

13

Phasors

14

Huygens’ wave construction

• Fresnel integral• phasors shorter / rotate more

quickly at distance to give spiral

15

Fermat’s principle of least time

• refraction at a plane surfacePierre de Fermat (1601-1665)

x0 L

a

b

A B C

S

P

S

P

x

16

Fermat’s principle of least time

• refraction at a plane surfacePierre de Fermat (1601-1665)

x0 L

a

b

S

P

x

• light rays follow the path of least time between two points

S

P

17

Snell’s law of refraction

• refraction at a plane surface

x0 L

a

b

S

P

x

• light rays follow the path of least time between two points

Willebrord Snel van Royen(Leiden, 1580-1626)

S

P

18

Huygens’ wave construction

• mirages by refraction in the atmosphereChristiaan Huygens (1629-1695)

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Huygens’ wave construction

Christiaan Huygens (1629-1695)

• ocean waves parallel to shore

20

Huygens’ wave construction

Christiaan Huygens (1629-1695)

• ocean waves parallel to shorehttp://www.uwgb.edu/dutchs/EarthSC202Slides/

COASSLID.HTM

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Huygens’ wave construction

Christiaan Huygens (1629-1695)

http://geographyfieldwork.com/WaveRefraction.htm

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Huygens’ wave construction

Christiaan Huygens (1629-1695)

http://www.smccd.edu/accounts/bramalln/documents/waterwaves.pdf

http://www.dorsetphotos.co.uk

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