Wave Physics

1. Wave Physics PHYS 2023 Tim Freegarde

2. x x+δx 1 2 use physics/mechanics to write partial differential wave equation for system W Thermal waves (diffusion) insert generic trial form of solution W1 W2 find parameter values for which trial form is a solution

3. 26 DEC 2004 04:15Z =================== FROM: UN ENVOY SUMATRA Sumatra-Andaman earthquake 2004 TO: CHIEF SCI ADVISOR LONDON MAGNITUDE 9.1 EARTHQUAKE ALONG INDIA-BURMA SUBDUCTION ZONE. 1200KM FAULT LEAVING KM-WIDE RIDGES AND TROUGHS. 30 CUBIC-KM WATER DISPLACED. NOAA SATELLITE RADAR REPORTS +2HRS WAVE HEIGHT 0.6M +3HRS WAVE HEIGHT 0.4M PLS ADVISE ++ UTMOST URGENCY ++ Tsunami Inundation Mapping Efforts NOAA/PMEL - UW/JISAO

4. 26 DEC 2004 04:15Z =================== FROM: UN ENVOY SUMATRA Sumatra-Andaman earthquake 2004 TO: CHIEF SCI ADVISOR LONDON MAGNITUDE 9.1 EARTHQUAKE ALONG • Maldives INDIA-BURMA SUBDUCTION ZONE. • Seychelles 1200KM FAULT LEAVING KM-WIDE RIDGES AND TROUGHS. 30 CUBIC-KM WATER DISPLACED. • Mauritius/Reunion NOAA SATELLITE RADAR REPORTS +2HRS WAVE HEIGHT 0.6M +3HRS WAVE HEIGHT 0.4M PLS ADVISE ++ UTMOST URGENCY ++ Uwe Dedering / Wikipedia Commons

5. Sumatra-Andaman earthquake 2004 • Maldives • Seychelles • Mauritius/Reunion Uwe Dedering / Wikipedia Commons UN Office for the Coordination of Human Affairs

6. Sumatra-Andaman earthquake 2004 Tsunami Inundation Mapping Efforts NOAA/PMEL - UW/JISAO UN Office for the Coordination of Human Affairs • NOAA radar was experimental • data analysis and wave simulation were not possible until days later • 275,000 people perished

7. general wave phenomena waves in three dimensions waves from moving sources wave equations, derivations and solution WAVE EQUATIONS & SINUSOIDAL SOLUTIONS sinusoidal wave motions operators for waves and oscillations complex wave functions Huygens’ model of wave propagation interference WAVE PROPAGATION Fraunhofer diffraction longitudinal waves continuity conditions BEHAVIOUR AT INTERFACES boundary conditions SUPERPOSITIONS linearity and superpositions Fourier series and transforms Wave Physics FURTHER TOPICS further phenomena and implications http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7

8. 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 Wave propagation • 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 • Huygens reflection, refraction and diffraction • reflection and transmission at interfaces • string motion from initial conditions

9. ψ W W δx x-δx x x+δx x A frayed guitar string

10. combine forward and reflected waves to give total fields for each region Reflection at an interface apply continuity conditions for separate components hence derive fractional transmission and reflection

11. for a boundary at between regions A and B: Continuity conditions • transverse waves on a string: • electromagnetic waves: • sound waves: • thermal waves: non-normal incidence:

12. various derivations and forms • typically: • one condition derived from balance of forces • conservation of momentum Significance of continuity conditions • the two conditions combined • conservation of energy Transverse waves on a string • energy density: •  power: where

13. h(x) δx x x v Energy of waves on a string δy

14. at interface between two media: Impedance • transverse waves on a string: • sound waves: • thermal waves: • electromagnetic waves:

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

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