Wave Physics

1. Wave Physics PHYS 2023 Tim Freegarde

2. local and macroscopic definitions of a wave Coming up in Wave Physics... • 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

3. use physics/mechanics to write partial differential wave equation for system • waves are collective bulk disturbances, whereby the motion at one position is a delayed response to the motion at neighbouring points Wave equations • propagation is defined by differential equations, determined by the physics of the system, relating derivatives with respect to time and position insert generic trial form of solution e.g. find parameter values for which trial form is a solution • but note that not all wave equations are of the same form

4. use physics/mechanics to write partial differential wave equation for system • shallow waves on a long thin flexible string Solving the wave equation • travelling wave insert generic trial form of solution • wave velocity find parameter values for which trial form is a solution

5. local and macroscopic definitions of a wave So far in Wave Physics... • 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

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

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

8. today’s lecture: • local and macroscopic definitions of a wave Coming up in Wave Physics... • 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

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

10. Sinusoidal waves ω z • simple harmonic motion • circular motion where 10

11. occur when source is rotating or performing SHM Sinusoidal waves • 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

12. Sinusoidal waves • wavenumber • spectroscopists’ at , wavenumber • wavelength 12

13. Sinusoidal waves • angular frequency • frequency • period at , 13

14. x x Velocities of waves on a string • phase velocity • (group velocity) • transverse string velocity

15. δx x x Energies of waves on a string δy • kinetic: • potential:

16. 26 Dec 2004 • magnitude 9.15; 275,000 perished Sumatra-Andaman earthquake 2004 • 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

17. magnitude 9.15; 275,000 perished Sumatra-Andaman earthquake 2004 • 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