THE UNIVERSITY OF AKRON 3650:320 - Waves
TEXT: Vibrations and Waves in Physics
Iain G. Main
Cambridge University Press
(3rd ed, 1993)

Instructor:  Peter Henriksen
Phone:  972-6054; Office:  Room 10, Ayer Hall
Office Hours:  10:30-11:00 Tue., Thurs., and Fri. or by appointment

Introduction

    An understanding of waves and vibrations is important for a general understanding of physics because many physical phenomena, electromagnetism, optics, and quantum mechanics for example, can only be understood in terms of waves. One of the goals of the course is to stress the underlying unity in several branches of physics without necessarily delving into the details of those branches of physics. This course includes topics in mechanics, electricity, optics, solid state physics, wave mechanics, and nonlinear dynamics. The point of including these topics is to stress the underlying commonality of waves in these areas of science.

Course Outline

    The topics and materials for the course are included in the following chapters of the text: 1 – 12, 14 – 15, and 17 – 18. Most, but not all of the topics in each chapter will be discussed. If there is a need to review background material before discussing a particular topic, you input will be needed to determine how much review is necessary.

Simple and Damped Harmonic Motion
    Mechanical and electrical oscillators, superposition of two SHOs, damped motion of mechanical and electrical oscillators, resonance, logarithmic decrement, relaxation time, and Q-value.

The Forced Oscillator
    Impedance, frequency dependence of phase angle between force, displacement, and velocity, Q-value as a measure of power absorption.

Coupled Oscillations and Normal Modes
    Spring coupled masses, normal coordinates and normal modes.

Transverse Wave Motion
    The wave equation, transverse waves on a string, reflection and transmission of waves, impedance matching.

Fourier Methods
    Fourier series and analysis of periodic functions, Fourier transforms, application to optical diffraction.

Waves in Optical Systems
    Interference and diffraction, Young’s experiment, multiple slits, interferometers.

Wave Mechanics
    De Broglie waves, Heisenberg’s uncertainty principle, Schrodinger’s time independent wave equation, Potential wells and electron tunneling, harmonic oscillator.

Non-linear Oscillations and Chaos
    Anharmonic oscillations, free vibrations of finite amplitude pendulum, thermal expansion of crystal, relaxation oscillator, chaos and period doubling, chaos in a non-linear electrical oscillator.

Waves at Boundaries and Interfaces
    Fresnel’s equations
Diffraction Theory
    Single slit diffraction, Young’s experiment, and multiple slit diffraction.

Classroom Activities

    Classroom time will be used for discussing end-of-chapter problems and reviewing background material needed to solve those problems. Whenever applicable, computers with symbolic math software (Maple) will be employed. Using Maple eliminates tedious mathematical calculations while emphasizing an understanding of the physical phenomenon related to the calculations. In particular, Maple will be used for solving differential equations and plotting their solutions; for examining the effect of damping and the frequency of driving forces; for looking at resonance; for making graphs and animating plots; and for Fourier analysis.

Quizzes and Grades

    There will be four quizzes during the semester; the forth quiz will be the final exam. Each quiz will be scored on the basis of 100 points and will be 18% of your final grade. Homework and learning to use Maple will count 28% of the final grade. Students whose names do not appear on the University’s official class list by February 2, 1999, will not be permitted to participate?attend class, take exams, or receive credit?in the class.

Bibliography
    1. Pain, H. J. “The Physics of Vibrations and Waves”, 4th ed., John Wiley and Sons, 1993, New York.
    2. Hirose, Akira, and Karl E. Lonngren, “ Introduction to Wave Phenomena”, John Wiley and Sons, 1985, New York.
    3. Crawford, Frank S., Jr., “Waves” McGraw-Hill, 1968, New York.

Homework Problems
    Ch. 1 2, 3, 4, 5, 6,
    Ch. 2  1, 2, 3, 4, 6, 9.
    Ch. 3 1, 2, 3, 4, 5, 8.
    Ch. 4  1, 2, 5.
    Ch. 5 1, 3, 4, 8, 11, 12, 17, 18.
    Ch. 6  1, 2, 3.
    Ch.7 1, 2, 3, 4, 5, 6, 8, 9.
    Ch. 8 1, 3, 6, 8.
    Ch. 9 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 16.
    Ch. 10 1, 2, 3, 4, 5, 6, 7.
    Ch. 11 1, 2, 3, 4, 5, 6, 7, 8.
    Ch. 12 2, 3, 7, 8, 10.
    Ch. 14 2, 3, 5.
    Ch. 15 2, 3, 4, 5.
    Ch. 17 1, 3, 4, 5, 7, 9, 10, 11.
    Ch. 18 3, 5, 6, 7, 9, 11, 12, 15, 16a.