Wave PhysicsPHYS 2023

Tim Freegarde

02 Principles of wave propagation2020-21

2

Coming up in Wave Physics...

• 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

• this lecture:

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Wave Physics

• a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points

Local/microscopic definition:

• speed of propagation is derived

static

dynamic

particles (Lagrange) fields (Euler)

equilibrium

SHM

eg Poisson’s equation

WAVES

4

Electromagnetic waves

• vertical component of force

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Electromagnetic waves

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

• electric field = force per unit charge (q2)

• vertical component of force

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Gravitational waves

a

• vertical component of force

• delay due to propagation speed of force

• gravitational field = force per unit mass (m2)

• centre of mass motion quadrupole radiation

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

• electric field = force per unit charge (q2)

• vertical component of force

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Gravitational waves

• 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

8

Wave Physics

• a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points

Local/microscopic definition:

• a time-dependent feature in the field of an interacting body, due to the finite speed of propagation of a causal effect

Macroscopic definition:

• speed of propagation is derived

• speed of propagation is assumed

static

dynamic

particles (Lagrange) fields (Euler)

equilibrium

SHM

eg Poisson’s equation

WAVES

9

Wave Physics

• a collective bulk disturbance in which what happens at any given position is a delayed response to the disturbance at adjacent points

Local/microscopic definition:

• speed of propagation is derived

• What is the net force on the penguin?

• For an elastic penguin, Hooke’s law gives

• If the penguin has mass , Newton’s law gives

• rest position

• displacement

• pressure

• elasticity

• density

• separation

• where

• area

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Penguin waves

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Wave equations

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

• 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

• but note that not all wave equations are of the same form

e.g.

12

Coming up in Wave Physics...

• 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

• today’s lecture:

Wave PhysicsPHYS 2023

Tim Freegarde