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