1. Wave Physics
PHYS 2023
Tim Freegarde

2. Coming up in Wave Physics...
today’s lecture:
local and macroscopic definitions of a wave
transverse waves on a string:
wave equation
travelling wave solutions
other wave systems:
electromagnetic waves in coaxial cables
shallow-water gravity waves
sinusoidal and complex exponential waveforms
energy in wave motions

3. Electromagnetic waves
vertical component of force
delay may be due to propagation speed of force (retarded potentials)
electric field = force per unit charge (q2)

4. simple harmonic motion
Sinusoidal waves ω z
simple harmonic motion
circular motion
where 4 4

5. Sinusoidal waves at , wavenumber spectroscopists’ wavenumber
wavelength 5 5

6. Sinusoidal waves
at ,
angular frequency
frequency
period 6 6

7. Sinusoidal waves occur when source is rotating or performing SHM
detected by resonant detectors
conveniently manipulated in differential equations
allow standing wave solutions
only real travelling wave solutions in dispersive systems
useful terminology for dissipative systems
complete set of orthogonal solutions in linear systems
convenient for energy/power calculations

8. Complex wave functionsφ
simple harmonic motion
circular motion

9. Dispersion in dissipative systemsW W δx x x
x+δx
x-δx

10. 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

11. Wave Physics
PHYS 2023
Tim Freegarde

12. Energy of waves on a string
h(x) v δy δx x x
kinetic:
potential:

13. Velocities of waves on a stringx x
phase velocity
(group velocity)
transverse string velocity

14. Sumatra-Andaman earthquake 2004
26 Dec 2004
magnitude 9.15; 275,000 perished
1200 km along India/Burma plate subduction zone
slip of 15 m sideways, several metres vertically
formed ridges 1.5 km high, trench kms wide
30 km3 water displaced
Tsunami Inundation Mapping Efforts
NOAA/PMEL - UW/JISAO

15. Sumatra-Andaman earthquake 2004
magnitude 9.15; 275,000 perished
1200 km along India/Burma plate subduction zone
slip of 15 m sideways, several metres vertically
formed ridges 1.5 km high, trench kms wide
30 km3 water displaced
ocean waves ~ 60 cm
25 m high near shore
NOAA

16. Deep water waves ε1 ε2 h(x) volume = h(x) (δx+ε2-ε1) δy v1 v2 δx x-δx

17. Deep water waves
h(x)
volume = h(x) (δx+ε2-ε1) δy v1 δx
x-δx x
x+δx x

18. Water waves Ocean waves Severn bore Kelvin ship wake Tsunami
theguardian.com
© Jason Hawkes / Getty Images
© Reuters / Mainichi Shimbun
Ocean waves
Severn bore
Kelvin ship wake
Tsunami