Waves & Energy Transfer
-both particles & waves can transmit energy
-particles change position to transmit energy ---> waves do not
Definition: Mechanical Waves - those consisting of periodic motion of matter
-i.e. sound or water waves
-require a material medium
Definition: Electromagnetic Waves - those that consist of oscillating electric
and magnetic fields that move at the speed of light through space
-i.e. light, radio and x-rays
Definition: Matter wave - wave-like behavior of particles, such as electrons
-use quantum mechanics to describe it
3 types of mechanical waves:
1. Transverse wave - causes particles in medium to vibrate to the direction of motion
i.e. piano and guitar strings
2. Longitudinal Waves - causes particles in a medium to move to the direction of the
wave
i.e. sound wave; fluids, liquids and gases usually transmit only longitudinal waves
3. Surface Waves - a mixture of transverse and longitudinal waves
i.e. movement of water at its surface
Definition: Wave Pulse - a single disturbance that travels through a medium
-each point along wave eventually comes to rest
Definition: Traveling Wave - one which moves as a periodic, repetitious disturbance
in a medium
-displays continuous simple harmonic motion
-each point along wave vibrates regularly
Measures of a Wave:
Definition: Period (T)- shortest time interval during which the motion repeats itself
Vertical Distance
Period
Time
Definition: Frequency (f) - # of complete vibrations per second measured at a fixed
point
1
f 
T
Definition: Wavelength - shortest distance between 2 points where the wave pattern
repeats itself (  or "lambda")
Definition: Amplitude (A) - maximum displacement from rest or equilibrium position
Definition: Crest - highest point of each wave motion
Definition: Trough - lowest point of each wave motion
-each crest (trough) is 1 wavelength from the next crest (trough)
Vertical Distance
Crest
Wavelength

Amplitude
Time
Trough
Definition: Wave Velocity - wavelength per period

or v    f
T
{aka “the universal wave equation”}
v 
-increase amplitude, increase work done by wave
> amplitude, > energy transferred by wave
-for waves of constant velocity...
rate at which energy is transferred (power) is proportional to (amplitude)2
P A2
ex.: if amplitude increases by factor of 2, rate of transferred energy increases by factor
of 4
Wave Interference:
-basic physics principle...
"2 objects cannot occupy the same space at the same time"
-not true of waves
-speed of mechanical wave does not depend on the amplitude or frequency of the wave
-depends on properties of the medium
-i.e. speed of water depends on depth; speed of sound in air depends on air temp.
-also, speeds of low & high frequency waves are the same (as long as material is same)
Waves at Boundary Between Media:
-an incident wave reaches a boundary between 2 media
-part of incident wave continues on in new medium w/ same
frequency-->transmitted wave
-part of wave moves backward from boundary in old
medium--->reflected wave
-if difference in media is small, amplitude of transmitted
wave will be almost as big as incident wave & amplitude of
reflected wave will be relatively small (most of energy
transmitted)
-if 2 materials are very different, most of energy will be
reflected
-whenever wave passes from less dense to more dense
medium, reflected wave is inverted
-whenever wave passes from more dense to less dense
medium, reflected wave is erect, not inverted
Superposition of Waves:
Principle of Superposition states:
"the displacement of a medium caused by two or more waves is the algebraic
sum of the displacements caused by individual waves"
-result of superposition is interference
-Constructive interference occurs when amplitudes are in same direction
-result is wave w/ larger amplitude than any individual wave
-Destructive interference occurs when amplitudes are in opposite direction
-as 2 pulses overlap, displacement is reduced
-waves are able to pass through one another unchanged
-2 pulses w/ equal but opposite displacements meet (destructive interference)--->find
one point that is undisturbed--->node
-2 pulses w/ equal displacements in the same direction meet (constructive interference)->find point of maximum amplitude--->antinode
-wave in which nodes and antinodes are stationary--->standing wave
Reflection of Waves:
-direction of waves is shown by ray diagrams
-a ray is a line drawn at a right angle to the crest of wave
-line drawn at right angles to a barrier is called the normal
-angle between incident ray and normal is angle of incidence  i
-angle between normal and reflected ray is angle of reflection  r
Law of Reflection states:
"angle of incidence is equal to angle of reflection"
Refraction of Waves:
-change in direction of waves at boundary between media is refraction
Light twists inward when entering medium
of higher index of refraction
Light twists outward when entering medium
of lower index of refraction
-when waves spread around edge of barrier (or hole)--->diffraction
Single-slit diffraction of water
waves
-if waves spread around 2 closely-spaced holes, diffraction occurs
-if constructive interference occurs, antinodes will line up along antinodal lines
-if destructive interference occurs, nodes line up along nodal lines
Double-slit diffraction of
water waves
Reflection & Refraction of Light
Law of Reflection:
angle of incidence = angle of reflection
-angles measured from normal
(perpendicular to surface)
-incident ray, reflected ray & normal all lie
on same plane
regular reflection
Definition: Regular Reflection - if light falls
on very smooth surface, reflected rays are
parallel to each other (as were the incident
rays)
Definition: Diffuse Reflection - rays are
reflected in many different directions
diffuse reflection
Refraction of Light:
Definition: Optically Dense - when speed of light in one medium is slower
than that in another
Definition: Refraction - change in direction or bending of light at boundary
between 2 media
-when angle of incidence = 0o , angle of refraction = 0o
-speed changes but passes straight through, along the normal
-when light travels into a medium where it travels faster, angle of refraction > angle of
incidence OR if light enters less optically dense medium, refracted rays bend away from
the normal
-if light enters more optically dense medium, refracted rays bend toward the normal
Definition: Index of Refraction (n) - ratio of the speed of light in a vacuum to
its speed into a material
Snell's Law:
"Light moving from smaller n to larger n is bent toward
normal & vice-versa"
ni sin i  nr sin r
-ni is index of refraction for incident medium
-nr is index of refraction for second medium
-  i &  r are angles of incidence & refraction
-refractive index (n) can be found by measuring angles of
incidence & refraction
-Snell's Law can be used to find the speed of light in a material (originating from a
vacuum)
c
ns 
vs
ns is the index of refraction of the material
c is the speed of light in a vacuum (3.00 x 108 m/s)
vs is the speed of light in the material
Definition: Total Internal Reflection - occurs when light passes from a more optically
dense medium to a less optically dense one at an angle so great that there is no
refracted ray
Definition: Critical Angle (  c )- occurs when the refracted ray lies along the boundary of
the medium surface
nr
ni
-any ray that reaches the boundary of medium at an angle greater than  c cannot leave
medium
-all of the light is reflected ---> total internal reflection
sin c 
Refraction
Refraction at the Critical Angle
r c
Air
Air
Total Internal Reflection
r c
Air
i
i
Glass
light ray
r c
Glass
Gl ass
light ray
light ray
-practical applications: fibre optics, internal body probes
Summary of Formulae:
ni sin i  nr sin r
ns 
c
vs
sin c 
nr
ni