Wave PhysicsTim 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 phenomena

Fraunhofer diffraction

longitudinal waves

BEHAVIOUR AT INTERFACES

continuity conditions

boundary conditions

SUPERPOSITIONSlinearity and superpositions

Fourier series and transforms

FURTHER TOPICS operators for waves and oscillations

further phenomena and implications

waves in three dimensions

http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7

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…

LECTURESthree a week for 10 weeks or soaccompanying lecture notes

eleven sheets of exercisesCOURSEWORK

hand in to School office20%

a: 5 short questionsEXAMINATION

b: 2 longer questions80%

CLASSESonce 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:

Pain Physics of Vibrations & Waves

good: right level and comprehensiveMain Vibrations & Waves in

Physicsreasonable, but dated and slim

French Vibrations and Waves quite good; concise

Crawford Waves (out of print)

Coulson & JeffreyWaves (out of print)

Feynman Lectures in Physics excellent – put on your Christmas list!

• for handouts, links and other material, see http://www.phys.soton.ac.uk/quantum/phys2023.htm

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

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Wave Physics – la Ola

• response to action of neighbour• delayed reaction

• waves are bulk motions, in which the displacement is a delayed response to the neighbouring displacements

ttxxftxf ,,

vtxftxf ,e.g.

8

Electromagnetic waves

20

21

4 r

qqF

1q

a

2q

• vertical component of force tar

qqtF

30

12 4

9

Electromagnetic waves

• delay may be due to propagation speed of force (retarded potentials)

20

21

4 r

qqF

1q

a

crtar

qqtF 3

0

12 4

2q

• vertical component of force tar

qqtF

30

12 4

• electric field = force per unit charge (q2)

10

Gravitational waves

1m

a

2m

• vertical component of force

• delay due to propagation speed of force

crtar

mmGtF 3

0

21

4

• gravitational field = force per unit mass (m2)

221

r

mmGF

• delay may be due to propagation speed of force (retarded potentials)

crtar

qqtF 3

0

12 4

• vertical component of force

• electric field = force per unit charge (q2)

• centre of mass motion quadrupole radiation

11

Gravitational waves

1m

2m

• vertical component of force

• delay due to propagation speed of force

crtar

mmGtF 3

0

21

4

• gravitational field = force per unit mass (m2)

• 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