wave physics phys 2023 tim freegarde. 2 coming up in wave physics... local and macroscopic...

Wave PhysicsPHYS 2023

Tim Freegarde

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

• today’s lecture:

3

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

5

Electromagnetic waves

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

• electric field = force per unit charge (q2)


6

Gravitational waves

a


• 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)


7

Gravitational waves


• 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 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 assumed

static

dynamic

particles (Lagrange)

fields (Euler)

equilibrium

SHM

eg Poisson’s equation

WAVES

9

Wave Physics




• 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

10

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.

11

Plucked guitar string

• displace string as shown

• at time t = 0, release it from rest• …What happens next?

12

Wave equations





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.

13

Waves on long strings

14

Solving the wave equation





solution

• shallow waves on a long thin flexible string

• travelling wave

• wave velocity

15

Travelling wave solutions





solution

• use chain rule for derivatives

where

• consider a wave shape at which is merely translated with time

16

General solutions





solution

• wave equation is linear – i.e. if

are solutions to the wave equation, then so is

arbitrary constants

• note that two solutions to our example:

17

Particular solutions





solution

• fit general solution to particular constraints – e.g.

x

18


x

19


? xL

0,xy txy ,

?

20


xL

txy ,

x x L-xL+x

xy

xy

xLy

xLy

wave physics phys 2023 tim freegarde. 2 coming up in wave physics... local and macroscopic...

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