Wave Physics Tim Freegarde School of Physics & Astronomy University of Southampton

2 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 operators for waves and oscillations further phenomena and implications waves in three dimensions

3 Wave Physics principal characteristics of waves and wave propagation optics, sound, musical instruments, quantum waves introduction to electromagnetic waves, quantum mechanics a few diversionary examples… LECTURES three a week for 10 weeks or so accompanying lecture notes eleven sheets of exercises COURSEWORK hand in to School office 20% a: 5 short questions EXAMINATION b: 2 longer questions 80% CLASSES once a week four groups

4 Books and resources exercises and classes lectures, hand-outs and your own lecture notes textbooks - some suggestions: You should expect to refer to: PainPhysics of Vibrations & Waves good: right level and comprehensive MainVibrations & Waves in Physics reasonable, but dated and slim FrenchVibrations and Waves quite good; concise CrawfordWaves (out of print) Coulson & JeffreyWaves (out of print) FeynmanLectures in Physics excellent – put on your Christmas list! for handouts, links and other material, see

5 Wave Physics practical manifestations: general description of how physical systems change time-dependent field theory Why waves? sound light water ripples, breakers, ship waves radar and atmospheric sounding seismology electrical signals quantum mechanics STATIC EQUILIBRIUM eg Poisson’s equation DYNAMIC SHM WAVES FIELDS (Euler)PARTICLES (Lagrange)

6 Wave Physics – la Ola

7 response to action of neighbour delayed reaction waves are bulk motions, in which the displacement is a delayed response to the neighbouring displacements e.g.

8 Electromagnetic waves vertical component of force

9 Electromagnetic waves delay may be due to propagation speed of force (retarded potentials) vertical component of force electric field = force per unit charge ( q 2 )

10 Gravitational waves vertical component of force delay due to propagation speed of force gravitational field = force per unit mass ( m 2 ) delay may be due to propagation speed of force (retarded potentials) vertical component of force electric field = force per unit charge ( q 2 ) centre of mass motion  quadrupole radiation

11 Gravitational waves vertical component of force delay due to propagation speed of force gravitational field = force per unit mass ( m 2 ) centre of mass motion  quadrupole radiation coalescing binary stars:neutron stars, ~1.4 solar mass separation few tens of km several rotations per second stars coalesce after minutes detector is laser interferometer several km in size