Notes on
Waves
Notes on Waves
• Waves are ENERGY!
• Travel through medium (Electromagnetic
waves can travel through vacuum.)
• Medium doesn’t move, only energy travels
Two Types of Waves
• Transverse – oscillates perpendicular to
the direction of travel
• Longitudinal – oscillates parallel to the
direction of travel (AKA Compressional)
Notes on Waves
Properties of Transverse Waves
• Crest – the high point of the wave
• Trough – the low point of the wave
• Wavelength – the distance from crest
to crest, or trough to trough.
• Amplitude – the height of the wave,
from midpoint (equillibrium) to crest, or
midpoint to trough
There are 2 ½ waves in the above wave train.
Examples of Transverse Waves
• Water waves; wave on a string;
electromagnetic waves (e.g. radio waves,
television signals, infrared waves, visible
light, ultraviolet radiation, microwaves,
x-rays); S-waves (earthquakes)
Notes on Waves
Properties of Longitudinal Waves
• These waves must travel through a
medium
• Compression – regions where the
molecules in the medium are bunched
together
• Rarefaction – regions where the molecules
in the medium are spread apart
• Wavelength – the distance from
compression to compression
• Amplitude – the distance that any one
molecule is pushed away from equillibrium
Examples of Longitudinal Waves
• Waves through a slinky, sound waves,
shock waves, P-waves (earthquakes)
Earthquake
Damage
Vertical
S-waves
Lateral
S-waves
Notes on Waves
Period & Frequency
• Period – How long it takes for a single
wave cycle; measured in seconds,
minutes, hours, days, etc. (abbr.= T )
• Frequency – The number of wave cycles
in one second; measured in Hertz
1 Hz = 1 cycle/s (abbr. = f )
• f = 1/T and T = 1/f
Notes on Waves
Period & Frequency
Example problem : An ocean wave has a
period of 8 seconds. What is the frequency
of that wave?
f = 1/T = 1/ 8 seconds = 1/8 Hz = 0.125 Hz
Notes on Waves
Wave Speed
Liquids at 25°C
Waves travel at
different speeds
through different
media.
Gases
Material
Material
v (m/s)
Glycerol
1904
Sea water
1533
Water
1493
Mercury
1450
Solids
v (m/s)
Material
v (m/s)
Diamond
12000
Hydrogen (0°C)
1286
Pyrex glass
5640
Helium (0°C)
972
Iron
5130
Aluminum
5100
Air (20°C)
343
Brass
4700
Air (0°C)
331
Copper
3560
Gold
3240
Notes on Waves
Wave Speed
• Wave speed = wavelength x frequency
• Wave speed [v] is measured in m/s,
cm/s, km/s, km/hr, etc.
• Wavelength [λ] is measured in m, cm,
km, etc.
• So
v = λ•f
Notes on Waves
Wave Speed
Example problem
A blue whale
bellows in the
deep ocean
with a frequency of 15 Hz. If the wave has a
length of 100.3 m, what is the speed of
sound in the ocean?
Notes on Waves
Waves Behavior
o Reflection – when waves bounce off of a surface
o Refraction – when waves change speed (and
often direction) as they travel through different
media.
o Diffraction – when waves bend around corners
o Interference – when waves interact with other
waves
• Constructive Interference – when two (or more)
waves meet to make a bigger wave
• Destructive Interference – when two (or more)
waves meet to make a smaller wave
Notes on Waves
Reflection – when waves bounce off of a surface
• The angle of incidence equals the angle of
reflection.
Notes on Waves
Refraction – when waves change speed (and often
direction) as they travel through different media.
Refraction
• In which medium does light travel faster? (glass rod
appears bent)
Speed of Light
• v is the speed of light in
the new medium.
• n is the absolute index
• c= 3.0 x 108 m/s
of refraction.
• This is a measure of
• As the index increases
optical density.
the speed decrease.
• n is defined as the ratio
of the speed of light in a
vacuum to the speed of • Draw a graph for index
vs. speed.
light in a new medium.
Relative Index of Refraction
• n is the relative index of
refraction. If air is not
used, then remember
• nrel = n2/n1
• What is the relative index
when going from
diamond into lucite?

If nrel < 1 ;
speeds up

If nrel > 1 ;
slows down
Refraction
n(water)=1.33; n(glass)=1.50; n(air)=1.00
Calculate the speed
of light in water
and glass.
Vw = 2.26 x 108m/s
Vg = 2.00 x 108m/s
Refraction
n1- from
n2 - into
• When a wave slows down it bends closer to the
normal. {less to more – toward} n2>n1
• When a wave speed up it bends away from the
normal. {BLA – Big ―› Little – Away} n2<n1
Refraction
• If light rays bend closer to the normal when
slowing down, why does the glass rod seem
to bend away form the normal?
Apparent Depth
• Diverging rays enter
your eyes.
• You “think” in
Straight Lines.
R – Real Depth
A – Apparent Depth
• A virtual image
appears to come
from point y
Apparent Depth
• If the chest is 20 m below the surface at
what depth will the image appear?
• Assume nsea water = 1.34
Snell’s Law
•
n1sinθ1 = n2sin θ2
•
v1/v2 = λ1 / λ2
Example
A monochromatic light ray f = 5.09 x 1014 Hz is
incident on medium X at 55˚. The absolute
index of refraction for material X is 1.66
1.
2.
3.
What is material X?
Determine the angle
of refraction.
Determine the speed
of light in medium X.
Ex: Solution
The index of 1.66 is Flint Glass
To find the angle of
refraction use Snell’s
Law.
θ2= 30˚
To find the speed use
n=c/v.
v = 1.8 x 108 m/s
Notes on Waves
Diffraction – when waves bend
around corners
Notes on Waves
Interference – when waves interact with other
waves
• Constructive Interference – when two (or more)
waves meet to make a bigger wave
• Destructive Interference – when two (or more)
waves meet to make a smaller wave
Constructive
Interference
Destructive
Interference
Constructive and Destructive Interference
Notes on Waves
Doppler Effect
.
• The frequency (and wavelength) of a
wave changes depending upon how
the observer of the waves is moving
relative to the source of the waves
Notes on Waves: Doppler Effect
If the source is traveling towards the observer, the
wavelength is smaller and the frequency is higher than if the
observer and source had the same velocity.
YouTube Video
If the source is traveling away from the observer, the
wavelength is larger and the frequency is lower than if the
observer and source had the same velocity.
Notes on Waves: Doppler Effect
If the source is traveling towards the observer, the
wavelength is smaller and the frequency is higher than if the
observer and source had the same velocity.
Speed of Sound
in air = 343 m/s
If the source is traveling away from the observer, the
wavelength is larger and the frequency is lower than if the
observer and source had the same velocity.
Notes on Waves: Doppler Effect
Remember that the Doppler Effect applies to ALL
waves, including electromagnetic waves (light!).
When applied to light the Doppler effect is referred
to as either a Red Shift or a Blue Shift. It is by
studying this data from surrounding stars and
galaxies, that we know that the universe is
expanding. Most stars and galaxies exhibit a Red
Shift.
Notes on Waves
Good Numbers to Know:
Speed of sound in dry air @ 20˚C = 343 m/s
= 1,126 ft/s = 768 mph
Speed of light in a vacuum ~ 3.0 x 108 m/s
= 186,282 mph