WAVES
THE ELECTROMAGNETIC
SPECTRUM
Essential Question: What are the wave variables
and how do they relate to each other?
O Y G B I V
10-14
10-12
10-10
Gamma rays
R
Wavelength (λ) in
meters
Visible light
10-8
10-6
Ultraviolet
10-4
1020
1018
100
Infrared
102
Radio
TV, FM
1016
1014
1012
1010
108
AM
106
Frequency (f) in Hertz
High Energy
104
Microwave
X rays
1022
10-2
Low Energy
104
Waves are the result of a vibration
traveling from one location to another.
Waves are a method that enrgy uses to
travel from one location to another
velocity
Wave
Types of Waves
• Longitudinal or compression – vibrate
parallel to velocity. ex. Sound
• Transverse – vibrations perpendicular
to velocity. ex. Light and water waves
Frequency (f) in Hertz
Wavelength (λ) in meters
Vertical displacement
Crest
λ
(Waves per Second)
Amplitude
1 Hertz
1
second
Trough
2 Hertz
f
3 Hertz
Period and Frequency of Vibrations
• period – time (seconds) it takes
for 1 vibration (wave) to occur.
Unit: s
• frequency – number of
vibrations (waves) in a second
Unit: Hz or s-1
• f = 1/p AND p = 1/f
10Hz has a period of 1/10th of a
second
Period = 1/10 or 0.1
1 second
.1s .2s .3s .4s .5s .6s .7s .8s .9s 1s
f = 10 Hz
Electromagnetic Spectrum
Wave Uses
Relative Wavelength
What type of wave is it?
Use EM spectrum
1. λ = 2.90 x 10-8 m
2. f = 6.35 x 10 Hz
5. f = 1.52 x 1022 Hz
6. f = 3.99 x 108 Hz
3. λ = 7.01 x 10-6 m
4. λ = 9.40 x 10-14 m
7. λ = 8.34 x 10-10 m
8. f = 2.76 x 1010 Hz
Calculating frequency, wavelength, period and velocity
Symbol
Wavelength
λ
(Lambda)
Unit
Equation
Meters (m)
λ = v/f
f = v/λ
Frequency
f
Period
p
s
1/f
velocity of
light
v*
Meters per second
(m/s)
v=fλ
v = velocity
c
Meters per second
(m/s)
c=fλ
*Speed of light
(3.00 x10 8)
Hertz (Hz,
s-1)
f = 1/p
1. Draw continuous Y axis 4 sq from left side all the way
down
2. Calculate amplitude sq. + 1. Count down from the top
this many squares and draw your x axis all the way
across
3. Dots represent wavelength, dashes represent half a
wavelength: calculate # of sq. for wavelength and
make your dots (number of dots is determined by # of
vibrations)
4. In between each dot along your x axis make your
dashes
5. Calculate # of sq. for amplitude. Make a dot in
between dashes and dots up the correct number of
dots. Alternate this for crest and trough
6. Connect the dots to form your wave.
Speed of Light
Speed of light (c) in a vacuum =
8
3.00 x10 meters per second (m/s)
In any other medium you have to
calculate velocity
v=fλ
Vacuum
Water
How fast is the speed of light?
Going around the world 7.5 times a second
What is the wavelength?
What is the frequency?
What is the speed of the wave?
1) The wavelength of an x-ray is 4.32 x 10-11 m. What is
its frequency?
3.00x108 m/s
18 Hz
f = c/λ =
=
6.94
x10
4.32x10-11 m
2) Ultraviolet radiation from the sun has a frequency of
2.49 x 1016 Hz. What is its wavelength?
3.00x108 m/s
-8 m
=
1.20x10
λ = c/f =
2.49x1016 s-1
3) An infrared ray has a frequency of 1.01E10 Hz and a
wavelength of 2.95 x 10-2 m. What is the speed of the
wave?
1.01x1010 Hz x 2.95x10-2
=
2.98x108 m/s
Radio Stations
Radio stations transmit their
signal in megahertz (MHz)
1 megahertz = ? Hertz
106
98.5 MHz
1
x
106 Hz
1 MHz
=
9.85x 107
Hz
Radio Station’s Wavelength
What is the wavelength of these radio stations?
1)
2)
97.9 MHz (you have to convert to Hz
first)
9.79
x 107 Hz
λ = c/f
3.06 m
104.5
MHz
8
1.045 x10 Hz
λ = c/f
3) 1.053
105.3
x108 HzMHz λ = c/f
2.87 m
2.85 m
Interference
• Interference occurs when 2 waves
occupy the same space at the same
time.
• It can be “destructive” or
“constructive”, depending if the waves
are “in phase” or “out of phase”.
Interference
• Destructive
+
=
• Constructive
+
=
v=fλ
In a vacuum v = (c) speed of light
In any other medium you have to
calculate velocity
Faster =  f or ↓ λ
Slower = ↓f or  λ
Color Wavelengths
Color
λ
(m)
R
O
Y
G
B
I
V
7.00E-7 6.50E-7 6.00E-7 5.50E-7 4.70E-7 4.30E-7 4.00E-7
Baaaaaa
a!
Lambda!
A
B
C
D
2 Hertz
λ
f
3 Hertz
1 sec
1 sec
1 sec
1 sec
Period (time 1 swing)
Title
Period (time 1 swing) s
3
Title
No breaks!
0
String length (m)