Physics 8.03 Vibrations and Waves Lecture 1

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)

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 http://web.mit.edu/8.03

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

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

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)

Electromagnetic waves Light

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

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

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.

Today: SIMPLE HARMONIC MOTION Announcements Pick up take-home experiment kits Where: Room 4-335 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