Wave Physics PHYS 2023 Tim Freegarde 2020 21

Wave Physics PHYS 2023 Tim Freegarde 2020 -21 02 Principles of wave propagation

Coming up in Wave Physics. . . • this 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 2

Wave Physics Local/microscopic definition: • a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points • speed of propagation is derived particles (Lagrange) fields (Euler) static equilibrium eg Poisson’s equation dynamic SHM WAVES 3

Electromagnetic waves • vertical component of force 4

Electromagnetic waves • vertical component of force • delay may be due to propagation speed of force (retarded potentials) • electric field = force per unit charge (q 2) 5

Gravitational waves • vertical component of force • delay may bepropagation due to speed ofspeed force of force (retarded potentials) • electric field = force per unit (q 2)(m 2) gravitational field = force percharge unit mass • centre of mass motion quadrupole radiation 6

Gravitational waves coalescing binary stars: • neutron stars, ~1. 4 solar mass • vertical component of force • separation few tens of km several per second • delay due to propagation • speed of rotations force • stars coalesce after minutes • gravitational field = force per unit mass (m 2) • detector is laser interferometer several km in size • centre of mass motion quadrupole radiation 7

Wave Physics Local/microscopic definition: • a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points • speed of propagation is derived particles (Lagrange) fields (Euler) static equilibrium eg Poisson’s equation dynamic SHM WAVES Macroscopic definition: • a time-dependent feature in the field of an interacting body, due to the finite speed of propagation of a causal effect • speed of propagation is assumed 8

Wave Physics Local/microscopic definition: • a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points • speed of propagation is derived • What is the net force on the penguin? • area • rest position • For an elastic penguin, Hooke’s law gives • separation • displacement • If the penguin has mass , Newton’s law gives • pressure • elasticity • where • density 9

Penguin waves 10

Wave equations • waves are collective bulk disturbances, whereby the motion at one position is a delayed response to the motion at neighbouring points • propagation is defined by differential equations, determined by the physics of the system, relating derivatives with respect to time and position use physics/mechanics to write partial differential wave equation for system insert generic trial form of solution e. g. • but note that not all wave equations are of the same form find parameter values for which trial form is a solution 11

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 12

Wave Physics PHYS 2023 Tim Freegarde