wave physics phys2023phyweb.phys.soton.ac.uk/quantum/lectures/waves/waves20... · 2020. 11. 8. ·...

Wave PhysicsPHYS 2023

Tim Freegarde

12 Longitudinal waves2020-21

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 TOPICSwaves from moving sources

operators for waves and oscillations

waves in three dimensions

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

further phenomena and implications

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

• 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

4

Longitudinal waves

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

5

Longitudinal waves

ξ

x x+δx

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

rest

displaced

ξ+δξ

O

P Q

R

O

P′ Q′

RW(x)

6

Sound waves

• in gases, use pressure difference

7

Speed of sound in air

8

Speed of sound in air

9

Sound waves

• wave equation:

where the elasticity

ratio of specific heats

ambient pressure

• wave velocity:

www.youtube.com/watch?v=52UAEQfMTtU

air

helium

SF6

1.40

1.66

1.10

0.167

6.26

1.205

1000

135

340

kg m-3 m s-1

metals

water 1500

4000

10

Visual microphone

https://www.youtube.com/watch?v=FKXOucXB4a8http://news.mit.edu/2014/algorithm-recovers-speech-from-vibrations-0804

11

Thermal waves (diffusion)

x x+δx

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

1 2

Q1 Q2

Q

12

Thermal (diffusion) waves

13

Thermal (diffusion) waves

14

Traffic waves

Y Sugiyama et al., N J Phys 10, 033001 (2008)

• 22 vehicles on 230 m circumference

• requested to cruise at 30 kmh

• ‘jam’ propagates backwards at ~20 kmh

15

Wave Physics

WAVE EQUATIONS &

SINUSOIDAL SOLUTIONS

wave equations, derivations and solution

sinusoidal wave motions

complex wave functions

general wave phenomena

WAVE PROPAGATION

Huygens’ model of wave propagation

interference

Fraunhofer diffraction

longitudinal waves

BEHAVIOUR AT

INTERFACES

continuity conditions

boundary conditions

SUPERPOSITIONSlinearity and superpositions

Fourier series and transforms

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

FURTHER TOPICSwaves from moving sources

operators for waves and oscillations

waves in three dimensions

further phenomena and implications

Wave PhysicsPHYS 2023

Tim Freegarde