Physics 340
Audio Engineering
Review Sheet For Exam #1:
Some of the things you should know for the first
exam:
Human Hearing, the Fletcher Munson Effect, and the Decibel Scale:
The Simple Harmonic Oscillator:
- Requires a linear restoring force - Hooke's Law
- Be able to derive the equation of motion and solve it for the simple
harmonic oscillator
- Vibration at a single frequency
- Know (and be able to derive and use) the relationship between k, m, and the
angular frequency
- Total energy is proportional to the square of the amplitude
- Maximum kinetic energy = total energy
- Maximum kinetic energy is proportional to the square of the amplitude
- Be able to derive the equation for the driven harmonic oscillator
- Be able to derive the amplitude as a function of frequency for the simple
harmonic oscillator
- Understand resonance in the simple harmonic oscillator
Coupled Oscillators and Normal Modes:
- In most actual physical situations an oscillator is not isolated, but
rather interacts with nearby oscillators (is coupled)
- You should be able to write down free body diagrams and apply Newton's laws
for combinations of springs, masses, and pendulums and obtain the differential
equations of motion.
- Be able to solve the equations by addition, subtraction etc. and find the
normal mode frequencies and amplitude ratios
- Be able to use the general analytical approach to find normal mode
frequencies and amplitude ratios
- In a normal mode, all particles oscillate with the same frequency and a
constant amplitude.
- Any motion of a coupled oscillator can be viewed as linear combinations of
the normal mode oscillations.
- The number of normal modes of oscillation of a linear system is equal to
the number of particles. For a more general system it is equal to the number of
coordinates needed to fully describe the system (i.e. the number of degrees of
freedom.)
- For n coupled particles, be able to use/interpret the equations for the
amplitudes and frequencies that I would provide. Perhaps an essay question on
these equations?
- Be able to take the limit of the previously mentioned equations as the
number of particles becomes very large.
- One can define normal coordinates (which are linear combinations of
ordinary coordinates) for the system (one normal coordinate per degree of
freedom)
- If the normal mode oscillations are close together in frequency we observe
the classical "beating" pattern
- Be able to show that in a forced coupled system a large response occurs at
the normal mode frequencies. (Resonance)
Continuous Systems, The Wave Equation, and Fourier Analysis:
- Be familiar with the wave equation
- Be able to prove that a function I provide is a solution to the wave
equation
- Understand the normal modes and frequencies of a continuous string
- Line
- The period of the lowest mode is the time it takes a pulse to travel down
and back once along the string
- Any periodic vibration of the string is a superposition of normal modes
- Leads to concept of Fourier analysis
- Understand the simple complex analysis that we did and be able to use it
- Concept of orthogonal functions
- Be able to show that two functions are orthogonal on some interval
- Understand "Fourier's Trick"
- Know the expressions for the Fourier coefficients on symmetric intervals
and be able to use them to find the Fourier coefficients for simple periodic
functions
- Understand the theory of even and odd functions
- The integral of any odd function over a symmetrical interval is always
zero
Questions, Comments, and E-Mail
If you have any questions or
comments, you can send E-Mail to Dr. Greg Latta at
glatta@frostburg.edu
This page is under constant revision. Please check back often.
Thanks for stopping by!
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