Welcome to The School of Physics

1. Welcome to The School of Physics • What is physics? • What are the current challenges? • The universe: how and why? • Fundamental theory: explaining the particles, the fundamental constants, the laws of physics • Detecting gravitational waves: whole new unexplored spectrum • Technology: data storage, quantum computers, communication, mineral exploration technology • Precision measurements of universal constants • What do I do? • What do I expect of you?

2. Your Lecturers • Me, David Blair… Monday, Tuesday • More emphasis on demos. • Viet Dang ….Thursday • More emphasis on coursework. • Baptism of Fire!

3. Test 1 • Test 1      27 March (covers material to end of week 4) • READ SHEET, see WebCT • Waves and Optics              12 •  David Blair and Viet Dang • Heat and Thermodynamics   3 •   John Wojdylo.

4. Waves and Optics Text: Halliday, Resnick, Walker 8th Edition 6 chapters in 3 weeks Waves: Chapters 16,17 pp413-475 Optics: Chapters 33,34,35,36 pp889-1020 Goal of lectures: make the topics interesting…demos! highlight key topics, explain difficult bits study guide

5. How to Achieve • Learn from lectures • Study options • Study text book and WileyPLUS, sample problems • Work problems including weekly assignments • ppt slides (mine and official slides) on WebCT • Lectopia (last choice!)

6. What is a Wave • A travelling disturbance • A means of transporting energy from A to B • Action at a distance • An electron jumps state in a hydrogen atom on the star Alpha Centauri • 4 years later an electron jumps in the retina of your eye. • 50 milliseconds later a chemical charge wave reaches your brain

7. Types of Waves • Mechanical Waves • Sound, Seismic, Ocean waves, Vibrational Waves • Electromagnetic Waves • Radio, Optical, X-ray…… • Gravitational Waves • Likely to be discovered before you graduate! • Matter Waves • All matter behaves as waves (we think!) All waves described by the same equation!

8. General properties • Wave motion always described by a function like • F is some function that describes the shape of the wave • Often we think of sinusoidal waves because its easy and common

9. Non-sinusoidal waves • Shock waves from explosions • Earthquake seismic waves • Percussion instruments • Electromagnetic pulses • Gravitational wave burst from the birth of a black hole

10. Aspects of Waves • Zero rest mass, no medium, velocity c • Electromagnetic, gravitational • Finite rest mass, mechanical medium, v << c • Transverse or Longitudinal • Polarisation • Vertical, horizontal, x and y, (+ and x) • Energy exchange between two forms • Potential energy - kinetic energy • Electric energy - magnetic energy • Quantisation • All waves act like particles • All particles act like waves All waves transport energy, momentum and information DEMOS

11. Wave Demos • Mechanical waves (transverse) polarisation, energy transport through medium • Gravitational waves: energy transport through empty space • Mechanical waves: polarisation, reflection, velocity • Mechanical waves (longitudinal) • Slow Mechanical Waves.

12. Properties of Waves Amplitude: ym, often A Frequency, f, cycles/second = Hertz Angular frequency  = 2f radians/second Period T=1/f seconds, =2/T Wavelength meters Wavenumber 1/ cycles/meter Angular wavenumber k=2/radians/meter Phase kxtradians (or degrees) Relative phase 

13. DEMO Polarisation of radio Speed of a Wave If wave keeps its shape kx-wt = constant Differentiate: Hence Universal result:

14. Wave Speed in Stretched String DEMO: rope tension Simple observations waves go faster if tension is high. waves go slower in thick ropes compared with thin string for same tension Key parameters tension …a force mass density  mass per unit length Dimensional analysis • : MLT-2 ML-1: L2T-2. But v is LT-1 Hence guess

15. Wave Speed from F = ma Symmetrical wave pulse String moves in an arc of a circle Restoring force F Mass element Centripetal acceleration a =v2/R Using F=ma, Rearranging:

16. Rate of Energy Transmission Total energy constant Vertical velocity Max KE is of string element is Average KE per time element dt Total power = KE +PE Max KE Max PE

17. θ2 The Wave Equation Mass element of string F: Net y-force =  (slope difference between points 1 and 2) = {(dy/dx)2 - (dy/dx)1} ={d2y/dx2} Ma: dx (d2y/dt2) But v2= Partial derivatives! Read text or web for more complete derivation

18. Superposition of Waves • Overlapping waves add (algebraically) • They do not alter each other • Question: where does this fail • Shallow waves • Non-linear materials • Wave speed depends on amplitude.

19. Interference of Waves • Waves sum to • a maximum (constructive) • or minimum (destructive) • Use • Combined wave is • New phase, new amplitude (zero for 

20. Phasors • Vector representing wave amplitude and phase of wave Not direction! • Most useful for waves of same frequency  • Rotating at freq  • Place end to end to get resultant ym2 ymcos ymcos ym2 yr ym1 ym1   ymsin ymsin

21. DEMO Slow waves Beats Can crusher Standing Waves • Interference of two counter-propagating waves • Easiest made by reflection • Simple trig

22. A B A B A B Resonant Standing Waves By using carefully positioned supermirrors, can resonate light with L~ 108/2 Can build up intensity by factor of 104 At Gingin Gravity Centre we have beams of more than 1kW Optical Cavity

23. Assignment problems • Chap 16, #11 • Chap 16, #23 • Chap 16, #26 • Chap 17, #13 • Chap 17, #56 • Chap 17, #61 • Chap 17, #89

24. A quick reminder David Blair and I are innocent! Questions regarding your timetable, WileyPlus, tutorials, labs, clashes ... etc PLEASE talk to JOHN BROOKES! How to get hold of him? Room 5.04 on 5th floor p1101.coordinator@physics.uwa.edu.au Call 6488 7018 Stalk*him if you must!!!! * I do not endorse stalking in any form

25. Interference of Waves Waves sum to a maximum (constructive) or minimum (destructive) Use Combined wave is New phase, new amplitude (zero for 

26. Constructive Interference Demo Ripple tank In phase Amplitudes add together

27. Destructive Interference Out of phase Amplitudes cancel each other

28. Doppler Effect (17.9) JAVA demo http://www.colorado.edu/physics/2000/index.pl?Page=applets/doppler.html Wave machine demo

29. Equation for Doppler Effect (17.54) • Moving source, detector is stationary • If moving away • If moving towards

30. A completely fictional example...

31. Example (continued...) Going towards him Vsource = 216 km/h Police Police Going away from him Vsource = 216 km/h Always need a picture!

32. Solution Going towards Ben • Answer: ~ 607 Hz Going away from Ben • Answer: 425 Hz Vsource is 216 km/h 60 m/s

33. What about this case? Vsource = 60 m/s Police Observed frequency

34. Sound Waves • Expand spherically from a point source. • Imagine spherically expanding wavefronts • String: • Gas: • elastic term: bulk modulus of elasticity B • Inertia term: density  air (about 1kgm-3) Elastic term Inertia term

35. Δp Speed of Sound • Bulk modulus B • Negative: squeeze and it gets smaller • Change in pressure per fractional change in volume. • Read sample problem 17-1. When you clap, why does a stepped pyramid have a musical echo.

36. Describing Sound • Displacement amplitude sm s(x,t) = smcos(kx-t) • Pressure variation amplitude pm p(x,t) = pmsin(kx-wt) • Relation between pm and sm • pm = (v)sm • 90 degree phase shift between displacement and pressure

37. Sound Speed in Pipe As usual use F=ma Area A, pressure p, F= pA Use elements x,p,t x = vt Force: across x: F = -pA Massm = Ax = Avt Acceleration: a = v/t Hence -pA = Avt(v/t) Important step

38. Intensity and Power Flow • Energy transmission down a cable (lecture 2) • Acoustic Intensity • Power per unit area • Same equation -replace  (mass density of string) with  (density of medium) different displacement amplitude symbol

39. Sound Velocity ms-1, Bulk Modulus Pascals Demo Helium Density of helium 0.18kg/m3 Density of air 1.2kg/m3 End week 1, class 3

40. Measuring Sound Intensity • Range of human hearing 10-5m -10-11m • Intensity ~s2, dynamic range 1012 !! • Use log scale • Sound level  = (10dB)log(I/I0) • I0 = 10-12W/m2….lower limit of hearing • I=I0, =0dB, • I=1012I0, =120dB pain threshold, 1W/m2 End week 1 classes 1, 2

41. Beats Two waves Slightly different frequency. At x=0 s1 =smcos1t s2 =smcos2t Resultant s Used trig identity for cosA +cosB Beat occurs at the difference frequency (max for cos=+/-1) 500Hz, 501Hz, beat at 1Hz

42. DEMO: Standing Waves in 2-D Chladni Figures Sand shows nodes Every sound source has associated standing wave patterns Such standing waves are called NORMAL MODES