1. Wave Physics PHYS 2023 Tim Freegarde

2. 2 Thermal waves (diffusion) xx+δx 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 1 2 W1W1 W2W2 W

3. 3 Traffic waves Y Sugiyama et al., N J Phys 10, 033001 (2008) 22 vehicles on 230 m circumference requested to cruise at 30 kmh ‘jam’ propagates backwards at ~20 kmh

4. 4 Sumatra-Andaman earthquake 2004 Tsunami Inundation Mapping Efforts NOAA/PMEL - UW/JISAO 26 DEC 2004 04:15Z =================== MAGNITUDE 9.1 EARTHQUAKE ALONG INDIA-BURMA SUBDUCTION ZONE. 1200KM FAULT LEAVING KM-WIDE RIDGES AND TROUGHS. 30 CUBIC-KM WATER DISPLACED. +2HRS WAVE HEIGHT 0.6M +3HRS WAVE HEIGHT 0.4M NOAA SATELLITE RADAR REPORTS FROM: UN ENVOY SUMATRA TO: CHIEF SCI ADVISOR LONDON PLS ADVISE ++ UTMOST URGENCY ++

5. 5 Sumatra-Andaman earthquake 2004 Uwe Dedering / Wikipedia Commons 26 DEC 2004 04:15Z =================== MAGNITUDE 9.1 EARTHQUAKE ALONG INDIA-BURMA SUBDUCTION ZONE. 1200KM FAULT LEAVING KM-WIDE RIDGES AND TROUGHS. 30 CUBIC-KM WATER DISPLACED. +2HRS WAVE HEIGHT 0.6M +3HRS WAVE HEIGHT 0.4M NOAA SATELLITE RADAR REPORTS FROM: UN ENVOY SUMATRA TO: CHIEF SCI ADVISOR LONDON PLS ADVISE ++ UTMOST URGENCY ++ Maldives Seychelles Mauritius/Reunion

6. 6 Sumatra-Andaman earthquake 2004 Uwe Dedering / Wikipedia Commons Maldives Seychelles Mauritius/Reunion UN Office for the Coordination of Human Affairs

7. 7 Sumatra-Andaman earthquake 2004 NOAA radar was experimental data analysis and wave simulation were not possible until days later 275,000 people perished UN Office for the Coordination of Human Affairs Tsunami Inundation Mapping Efforts NOAA/PMEL - UW/JISAO

8. 8 Wave Physics WAVE EQUATIONS & SINUSOIDAL SOLUTIONS wave equations, derivations and solution sinusoidal wave motions complex wave functions WAVE PROPAGATION Huygens’ model of wave propagation interference general wave phenomenaFraunhofer diffractionlongitudinal waves BEHAVIOUR AT INTERFACES continuity conditions boundary conditions SUPERPOSITIONS linearity and superpositions Fourier series and transforms FURTHER TOPICS waves from moving sources operators for waves and oscillations waves in three dimensions http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7 further phenomena and implications

9. 9 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 Huygens reflection, refraction and diffraction reflection and transmission at interfaces string motion from initial conditions

10. 10 A frayed guitar string xxx+δxx-δx ψ W W δxδx

11. 11 Reflection at an interface combine forward and reflected waves to give total fields for each region apply continuity conditions for separate components hence derive fractional transmission and reflection

12. 12 Continuity conditions for a boundary at between regions A and B: transverse waves on a string:electromagnetic waves:non-normal incidence:sound waves:thermal waves:

13. 13 Significance of continuity conditions various derivations and forms typically:one condition derived from balance of forces conservation of momentum the two conditions combined conservation of energy Transverse waves on a string energy density:  power: where

14. 14 Energy of waves on a string x x h(x) δxδx v δyδy