Lecture 1
Properties of Waves, from Slinky Coils
to the Vacuum of Space
I. General Properties of Waves (Example: Slinky Waves)
A. wave: a "disturbance" which propagates through a "medium",
thereby transmitting energy from one point to another
1. slinky example: disturbance = sideways displacement
or compression of slinky coils
2. slinky example: medium = slinky coils
3. slinky example: energy = energy of motion
B. fundamental wave equation: v = lf
(relationship between the 3 fundamental parameters of a wave)
1. v = velocity of the wave (speed
of propagation of the disturbance)
2. l
= wavelength (distance between peaks or troughs or any two similar points
of the wave)
3. f = frequency (number of "wavelengths"
or peaks that pass a given point per unit time)
C. two basic wave types based
on the direction of the disturbance "oscillatory motion" ("motion" = "change
in physical quantity that is being 'disturbed'")
1. transverse wave = direction
associated with the disturbance "oscillatory motion" perpendicular
to the direction of the disturbance propagation
a. slinky example: sideways
displacement of slinky coils
b. other examples: surface
water waves, "s wave" type of seismic waves, electromagnetic waves
2. longitudinal wave = direction
associated with the disturbance "oscillatory motion" parallel to the direction
of the disturbance propagation
a. slinky example: compression
of slinky coils
b. other examples: sound
waves, "p wave" type of seismic waves
D. wave "shape" and amplitude
1. wave forms come in many different
varieties depending on the nature of the oscillatory disturbance that creates
the wave, for our purposes we limit the discussion to so called "sinusoidal
waves"
a. wave form = shape of wave as
observed when the disturbed quantity is plotted against position
b. slinky examples: displacement
of slinky relative to its equilibrium position (transverse example) -or-
number of coils per unit length (longitudinal example) both plotted as
a function of position
c. other examples: surface
water wave - displacement of surface as a function of position; sound wave
- pressure as a function of position; strength of electric and magnetic
fields as a function of position
2. sinusoidal waves = wave form
produced by an "oscillatory disturbance" that can be described by the same
mathematical equations that describe the motion of a mass on a spring:
"simple harmonic motion"
a. plot of the quantity being
disturbed as a function of position produces a wave form that exactly resembles
the trigonomic sine or cosine function plotted against angle (slinky example:
plot of displacement of slinky relative to its equilibrium position when
the end of the slinky undergoes simple harmonic motion)
b. amplitude = maximum change
of the quantity disturbed (slinky example: maximum displacement of
the slinky relative to its equilibrium position)
E. interference of waves:
discussion limited to waves for which the amplitudes add linearly (most
waves)
1. constructive interference:
waves which combine "in step" (peak adds to peak, trough to trough); two
wave with same amplitudes produce a resultant wave with twice the original
amplitudes
2. destructive interference:
wave which combine "out of step" (peak adds to trough); two wave with the
same amplitudes produce a resultant wave with zero amplitude, in
effect the two waves cancel each other out
3. any phenomena which exhibits
interference may be described as a wave phenomena
II. Electromagnetic Waves (Light, Radio, Ultraviolet, Infrared, Microwave,
X-rays, g-rays,...)
A. the nature of light, Newton to Einstein
1. Newton: corpuscular theory - light as particles, explained
much of the phenomena associated with the behavior of light such as the
law of reflection
2. later researchers showed that light undergoes interference (double
slit experiment) and obeys the fundamental wave equation (c = lf
) where c = speed of light = 300,000,000 meters per second
3. Maxwell: 1862 - unified
magnetic and electrical phenomena with his linear electromagnetic field
theory and predicted electromagnetic waves which propagate at the speed
of light
4. Einstein: explained the
"photo-electric effect" by describing light as particles called photons
B. electromagnetic waves: disturbance in the electric and magnetic
fields around an accelerating (oscillating) charge, the directions
of the electric and magnetic field lines associated with the wave are perpendicular
to the direction of propagation of the disturbance (transverse waves),
the disturbance propagates at the speed of light = c
1. light = electromagnetic wave,
other E&M waves differ only in wavelength (or frequency)
2. E&M waves were thought
to propagate through a special medium called the ether, but around
the turn of the 20th century it was shown that there is NO ether - we now
think of E&M waves as a disturbance in the electric and magnetic fields
around an accelerating charge that propagates through the fields at the
speed of light
3. E&M spectrum: radio
- l = km
to m; microwave - l =
cm; infrared - l = mm;
visible light - l =
500 nm; ultraviolet - l = 100 nm;
X-rays & g-rays
- l = nm