Introductory Physics © James J DeHaven, Ph.D., 2010-2011, Chap 16
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Chap 16
Waves
Final Version of review
notes
Introductory Physics © James J DeHaven, Ph.D., 2010-2011, Chap 16
To start off: Here is a reprint from the table of contents
Waves
Characteristics of waves
Reflection
Refraction
Diffraction
Interference
Description of waves
Solitary
Transverse
Longitudinal
Wave parameters
Wavelength
Frequency
Phase velocity
Standing Waves
Eigenvalues
Tones and overtones
Idea of Fourier Spectrum
Analysis of a guitar
Calculus: Solving 1D wave equation
Sound
Description
Intensity and Intensity level
Pitch
Quality
Hearing
Recording Sound
Digitizing Sound
CDʼs vs. Records
Beats
Appliccation to Radio
Doppler Effect
Appl to cosmology
First--You do not need to be able to solve the 1D wave equation at this time
Parameters the goven waves
wavelength denoted by the greek letter lambda (λ)
phase velosity denoted by v
frequency denoted by f
The equation that relates the three together is
v = λf
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Introductory Physics © James J DeHaven, Ph.D., 2010-2011, Chap 16
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The velocity depends on the nature of the medium and its expression always has the form of square root of
elasticity factor divided by density factor. For a solid it is:
E
v=
ρ
where E is the elastic modulus and ρ is the density.
For fluids we get:
B
v=
ρ
where B is the bulk modulus and ρ is the density.
For a thin string, the speed is:
Ft
v=
µ
where Ft is the tension and µ is the so-called linear density, the mass of the string divided by its length
What attributes or characteristics tell you that you have a wave?
Reflection
Refraction
Diffraction
Interference
Reflection
A wave bounces off a surface--a surface being defined as any boundary between 2 well-defined media.
There is a simple formula for the “bounce” or reflection angle. Angle of reflection = angle of incidence.
For wave angles we always count the angle as the one between the velocity vector of the wave front and the
normal to the surface that the wave is incident upon.
Refraction
Introductory Physics © James J DeHaven, Ph.D., 2010-2011, Chap 16
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Refraction arises from the tendency of waves to change speed when moving from one medium top another.
When the wave crosses a boundary and enters the new medium, its velocity changes according to the
equation:
v1 sin θ1
=
v2 sin θ 2
Diffraction
This phenomenon is one in which waves can go around boundaries. The KEY to understanding diffraction
is the relative size of the wavelength and the object about which it diffracts. If the wavelenght substantially
exceeds some dimension of the object, then diffraction is relatively easy to observe. If it is smaller then
diffraction is not as readily observable.
Interference.
When waves “intercept” each other, they do algebra. That is to \say their displacements add algebraically.
If crets and troughs are overlapping then the waves reiforce each other and you get constreuctive
interference, and when crests overlap troughs, you get destructive interferencce.
Try to be prepared to discuss these by analyzing wave phenomena in your everyday life. and knowing
concrete example of each characteristic. You can also cite experiences from the laboratory.
Wave Types
Distinguish between a pulse (solitary wave) and a CW (coninuous wave) wave.
Distinguish between a transverse and longitudinal wave, with examples of course.
Standing Waves: Waves on a string
What is a standing wave and why and how is it formed?
How to derive the equation(s) for the frequencies of standing waves on a string (such as a guitar string
nv
f=
2L
n Ft
f=
2L µ
What are nodes, antinodes, the fundamental, overtones, boundary conditions--what is the root cause that
forces s stringed instrument to choose only certain values of frequency (eigenvalues)? How do the
Introductory Physics © James J DeHaven, Ph.D., 2010-2011, Chap 16
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equations for standing waves instruct you about how to play the guitar (or violin, or harp, or whatever)?
What is the difference between pitch and timbre, and how does this connect to the concepts associated with
standing waves/ In particular, what is a Fourier spectrum, and what does this have to do with timbre. How
do all of these affect the human perception of sound.
We discussed this last idea at great length and our discussion was a wide ranging one, covering
areas as diverse as euphonious sounds and pleasant chords to sound recording and the advent of the CD.
how fo we measure the loudness of sound> What is the frequency range of the human ear and
where is our hearing most acute? What is the loudness range of the human ear. Can a sound be too loud?
Can a sound be too soft? How soft is too soft?
Distinguish between intensity and intensity level. For intensity level be able to move back and forth
between
I
β = 10 log
I0
and
I = I 0 10
β
10
Finally, you need to understand the concept of Beat frequency with perhaps an example or two
And you need to understand the idea of the doppler effect, again with examples. One important example is
how the Doppler shift of the light from distant galaxies informs our ideas about cosmology.