1. Wave Physics
PHYS 2023
Tim Freegarde

2. Wave propagation transverse motion of taut string
use physics/mechanics to write partial differential wave equation for system
e-m waves along coaxial cable
shallow-water waves
flexure waves
string with friction
travelling wave:
general form
sinusoidal
insert generic trial form of solution
complex exponential
damped
standing wave
soliton
speed of propagation
find parameter values for which trial form is a solution
dispersion relation
string motion from initial conditions

3. Wave propagation in changing media
today’s lecture:
Huygens’ construction
gradual change:
refraction
interface between media:
refraction; continuity conditions
obstacles:
1-D: boundary conditions
2/3-D: diffraction

4. Wave propagation waves are collective bulk disturbances, in which
motion is a delayed response
to neighbouring motions
when propagation follows multiple routes
the amplitudes are added
waves propagate via all possible routes

5. Huygens’ wave construction
wavefronts propagate from initial disturbance in all directions
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
Christiaan Huygens ( )

6. Huygens’ wave construction
two point sources

7. Huygens’ wave construction
two point sources
five point sources

8. Huygens’ wave construction
five point sources
21 point sources

9. Huygens’ wave construction
propagation from a point source
Christiaan Huygens ( )

10. Huygens’ wave construction
reflection at a plane surface
Christiaan Huygens ( )

11. Huygens’ wave construction
refraction at a plane surface
Christiaan Huygens ( )

12. Huygens’ wave construction
refraction at a plane surface
Christiaan Huygens ( )

13. Phasors

14. Huygens’ wave construction
Fresnel integral
phasors shorter / rotate more quickly at distance to give spiral

15. Fermat’s principle of least timeB C b P P x L x
refraction at a plane surface
Pierre de Fermat ( )

16. Fermat’s principle of least time
Pierre de Fermat ( ) S S a
light rays follow the path of least time between two points b P P x L x
refraction at a plane surface

17. Snell’s law of refraction
light rays follow the path of least time between two points
Willebrord Snel van Royen
(Leiden, ) b P P x L x
refraction at a plane surface

18. Huygens’ wave construction
mirages by refraction in the atmosphere
Christiaan Huygens ( )

19. Huygens’ wave construction
ocean waves parallel to shore
Christiaan Huygens ( )

20. Huygens’ wave construction
ocean waves parallel to shore
Christiaan Huygens ( )

21. Huygens’ wave construction
Christiaan Huygens ( )

22. Huygens’ wave construction
Christiaan Huygens ( )
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