1. Physics 8.03 Vibrations and Waves
Lecture 1

2. Organizational things
Staff
Nergis Mavalvala (L)
Walter Lewin (R)
Patrick Varilly (tutor)
Grades
10 problem sets = 25% total
Posted on Sundays, USUALLY due at 4pm Fridays
3 in-class exams = 15% each
Exam reviews will be held, look at web site for details
1 final exam = 30%
During finals week
Take-home experiments (incomplete)

3. More organizational things: The Website
All course information appears on the 8.03 web site at
Reload often, the web pages will be updated nearly every day
Don’t wait till last minute to download, web servers are not always cooperative

4. Outline of course
Mechanical oscillators (and some electrical circuit analogs)
Mechanical waves
Electromagnetic waves
Optical phenomena

5. Why oscillations and waves? And all semester long?
Because oscillations in nature are ubiquitous (and we know how to solve the eqn. of motion)
Periodic motion + circular orbits
Optical, electrical and mechanical structures + resonance
Because waves pervade the universe
Mechanical waves (sound, water, phonons…)
Electromagnetic waves (radiation, visible light…)
Matter waves (atoms, BECs, QM)
Gravitational waves (neutron stars, black holes, GR)
Circular vs. periodic: demo 4
Sound waves: Violin phasing audio clip
Matter waves: BEC video clip
Gravitational waves: BH-BH binary simulation

6. Sound waves Phasing in music
Steve Reich: “Violin Phase” (1967)
A repeated segment of music is played simultaneously by three violins at slightly different tempos (phases)
Musically gifted folks will notice that the violins come in and out of phase periodically
He discovered this when he was trying to play back an identical music piece with two tape recorders that ran at slightly different speeds (?)
Music clip from ECM records web site
(thanks to Prof. van Oudenaarden)

7. Electromagnetic waves Light

8. Matter waves Formation of a BEC
When a gas of atoms is cooled to absolute zero, the atoms congregate in the ground state
The wave functions of the particles overlap and their phases get locked to each other
All the atoms are in a single quantum state and form a strong matter wave
The laser power changes the shape of the potential in which the atoms are trapped
Animation from Prof. Ketterle’s web site

9. Gravitational waves Collision of a pair of black holes
Two black holes coalesce
The emerging GWs carry signature of the quasi-normal oscillation mode of the final black hole
Animation thanks to NCSA relativity group

10. Final Exam HARMONIC OSCILLATORS Free or Damped Driven  RESONANCE
OPTICS
Multiple Sources
Interference
Diffraction
Final Exam
Exam 1
Exam 3
Exam 2
COUPLED OSCILLATORS
N = few  NORMAL MODES
N = many (continuous media)
MECHANICAL WAVES
wave equation…
ELECTROMAGNETISM
EM WAVES in vacuum
EM sources  RADIATION
EM waves in media
(conductors + dielectrics)
RESONANCE  Tacoma Narrows video
NORMAL MODES  Wilburforce pendulum
LIGHT  polaroids + birefringence  light meets matter
Calcite: ordinary and extraordinary waves with orthogonal polarization
Mica + glass disks: birefringence causes different retardation for different wavelengths of light. Some of the retarded waves interfere constructively others destructively. So color changes as analyzer picks out components at different frequencies.
Linearly polarized light enters mica, exits circularly polarized. Only the components along direction of analyzer will pass through to observer.

11. Today: SIMPLE HARMONIC MOTION
Announcements
Pick up take-home experiment kits Where: Room When: Thursday Feb. 05, 2 – 4pm (after lecture) Tuesday Feb. 10, 10am – noon or 2 – 4pm
Problem set 1 is due Friday February 13
Equation of motion for SHM
Solutions to equation of motion
Harmonic functions
Complex numbers
(Periodic functions)
Energy in oscillators
Conservative forces, quadratic potentials and SHM