Rochester Institute of Technology
Rochester New York
College of Science
Department of Physics
Course 1017-318
1.0
Title: Vibrations and Waves
Date: September 25, 2008
Credit Hours: 4
Prerequisite(s): 1017-312 or 1017-306, 1016-282 or 1016-273
Corequisite(s): Credit or co-registration in 1017-313
Credit or co-registration in 1016-283
2.0
Course information:
Classroom
Lab
Studio
Other
Contact hours
4
Quarter(s) offered (check)
_____ Fall __ __ Winter
Maximum students/section
50
__X__ Spring
_____ Summer
Students required to take this course: (by program and year, as appropriate)
Majors in the Department of Physics
Students who might elect to take the course:
Students majoring in Imaging Science, engineering, and others with the
appropriate background.
3.0
Goals of the course (including rationale for the course, when appropriate):
To communicate the idea that waves are the natural excitations of any medium
and that you should expect to meet waves in nearly all branches of physics.
Students will gain a basic understanding of the physics of vibrations and waves,
including simple and damped simple harmonic motion, the forced oscillator and
resonance, coupled oscillations and normal modes, transverse wave motion,
longitudinal waves, waves in more than one dimension, Fourier methods, nonlinear oscillations.
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4.0
Course description (as it will appear in the RIT Catalog, including pre- and corequisites, quarters offered)
1017-318
Vibrations & Waves
An introduction to the physics of vibrations and waves. (Prerequisites: 1017-312 or
1017-306, 1016-282 or 1016-273, Corequisites: Credit or co-registration in 1017-313,
credit or co-registration in 1016-283) Class 4, Credit 4 (S)
5.0
Possible resources (texts, references, computer packages, etc.)
5.1 Main, I. G. Vibrations and Waves in Physics, CUP.
5.2 French, A. P., Vibrations and Waves, Norton.
5.2 Pain H. L, The physics of Vibrations and Waves, Wiley.
6.0
Topics (Outline):
6.1 Harmonic motion (~7 lectures)
6.1.1 Simple harmonic oscillator (mass/spring system)
6.1.1.1 Justification (Taylor’s series around potential minimum)
6.1.1.2 General solution (sine/cosine) and initial conditions
6.1.1.3 General solution (complex exponential)
6.1.1.4 Energy
6.1.2 Damped harmonic motion
6.1.3 Forced damped harmonic motion
6.1.4.1 Resonance
6.1.4.2 Q factor
6.1.4.3 Phase angle
6.1.4 Periodic driving force
6.2 Fourier Series (~ 6 lectures)
6.2.1 Basis vectors, orthogonality, completeness (use analogy with 3D Cartesian
unit vectors)
6.2.2 Fourier sine / cosine series
6.2.3 Fourier exponential series
6.2.4 Fourier decomposition of wave pulse
6.2.4.1 Classical uncertainty relationship
6.2.5 Damped harmonic oscillator with periodic, but not sinusoidal, driving force
6.3 Coupled oscillators (~ 6 lectures)
6.3.1 Mass/spring system
6.3.1.1 Symmetric and anti-symmetric solutions
6.3.1.2 Normal frequencies
6.3.1.3 Normal coordinates
6.3.2 N coupled oscillators
6.3.2.1 Dispersion
6.4 Oscillations in continuous media (~ 6 lectures)
6.4.1 1D wave equation
6.4.1.1 Derivation of 1D wave equation for stretched string
6.4.1.2 Separation of variables
6.4.1.3 General properties of solution
6.4.1.4 Initial conditions
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6.4.1.5 Boundary conditions
Vibrating string
6.4.2.1 Superposition and Fourier series
6.4.2.2 Standing waves
6.4.2.3 Normal modes
6.5 Waves (one-dimensional) (~ 4 lectures)
6.5.1 One-dimensional traveling sinusoidal wave
6.5.1.1 Energy and intensity
6.5.2 Boundary effects (reflection, transmission)
6.5.3 Longitudinal waves
6.6 Wave pulses (~ 2 lectures)
6.6.1 Superposition of two waves
6.6.2 Phase and group velocity
6.6.3 Dispersion
6.7 Waves (two-dimensional) (~ 6 lectures)
6.7.1 Huygens Principle
6.7.2 Plane waves
6.7.2.1 Reflection and refraction
6.7.2.2 Double slit interference
6.7.2.3 Multi-slit interference
6.7.2.4 Diffraction
6.7.3 Applications
6.7.3.1 Mechanical waves
6.7.3.2 Electromagnetic waves
6.7.3.3 Matter waves
6.4.2
7.0
7.1
7.2
7.3
7.4
7.5
8.0
Intended learning outcomes and associated assessment methods of those outcomes
Learning outcome
Exams and
Homework
quizzes
assignments
Set up and solve the equations of simple harmonic
X
X
motion, damped and forced harmonic motion
Explain elementary concepts in waves: wavenumber,
X
X
frequency, travelling and standing waves, the role of
boundary conditions in determining allowed modes of
oscillation
Handle the mathematical description of sinusoidal waves
X
X
Approximate more realistic anharmonic vibrations with
X
X
SHO
Perform basic harmonic analysis of a wave and solve
X
X
problems involving pulses and wave groups
Program or general education goals supported by this course
8.1 To develop in students a basic understanding of the physical world and mathematical
descriptions of it.
8.2 To develop in students skill in applying mathematics to different physical situations.
8.3 To develop a capacity for critical thinking and analysis.
3/8/2016
9.0
Other relevant information (such as special classroom, studio, or lab needs,
special scheduling, media requirements, etc.)
10.0
Supplemental information - NONE
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