WAVESTHE ELECTROMAGNETIC SPECTRUM

Essential Question: What are the wave variables and how do they relate to each other?

Wavelength (λ) in meters

Frequency (f) in Hertz

10-14 10-12 10-10 10-8 10410-6 10-4 10-2 100 102

1022 1020 1018 1016 1014 1012 1010 108 106 104

Gamma rays

X rays

Ultraviolet Infrared Radio

Microwave

TV, FM AM

High Energy

Low Energy

R O Y G B I V

Visible light

Waves are a method that enrgy uses to travel from one location to another

Waves are the result of a vibration traveling 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

Crest

Trough

Amplitude 1

second

Vert

ical

dis

pla

cem

ent

3 Hertz

2 Hertz

1 Hertz

Wavelength (λ) in meters

Frequency (f) in Hertz

(Waves per Second)

λ

f

Period and Frequency of Vibrations

• period – time (seconds) it takes for 1 vibration (wave) to occur.

• frequency – number of vibrations (waves) in a second

• f = 1/p AND p = 1/f10Hz has a period of 1/10th of a second

Unit: Hz or s-

1

Unit: s

1 second

.1s .3s .5s .7s .9s.2s .4s .6s .8s 1s

10 Hzf =

Period = 1/10 or 0.1

Electromagnetic Spectrum

Wave Uses

Relative Wavelength

What type of wave is it?

Use EM spectrum1. λ = 2.90 x 10-8 m2. f = 6.35 x 10 Hz3. λ = 7.01 x 10-6 m4. λ = 9.40 x 10-14 m

5. f = 1.52 x 1022 Hz6. f = 3.99 x 108 Hz7. λ = 8.34 x 10-10 m8. f = 2.76 x 1010 Hz

Calculating frequency, wavelength, period and velocity

Symbol Unit Equation

Wavelength

λ(Lambd

a)

Meters (m) λ = v/f

Frequency f Hertz (Hz, s-

1)f = v/λ

f = 1/p

Period

p s 1/f

velocity of light v* Meters per

second (m/s)v = f λ

v = velocity

*Speed of light

(3.00 x10 8)

c Meters per second (m/s) c = f λ

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 LightSpeed of light (c) in a vacuum =

3.00 x108 meters per second (m/s)

Vacuum Water

In any other medium you have to calculate velocity

v=fλ

Going around the world 7.5 times a second

How fast is the speed of light?

1) The wavelength of an x-ray is 4.32 x 10-11 m. What is its frequency?

2) Ultraviolet radiation from the sun has a frequency of 2.49 x 1016 Hz. What is its wavelength?

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?

What is the wavelength?What is the frequency?What is the speed of the wave?

f = c/λ3.00x108 m/s

4.32x10-11 m= =

λ = c/f3.00x108 m/s

2.49x1016 s-1= =

6.94 x1018

Hz

1.20x10-8

m

1.01x1010 Hz x 2.95x10-2 m = 2.98x108 m/s

Radio StationsRadio stations transmit their signal in megahertz (MHz)1 megahertz = ? Hertz

106

98.5 MHz

1 MHz

Hzx =

1

106 9.85x 107 Hz

Radio Station’s WavelengthWhat is the wavelength of these

radio stations?

1) 97.9 MHz (you have to convert to Hz first)

2) 104.5 MHz

3) 105.3 MHz

9.79 x 107 Hz

λ = c/f 3.06 m

1.045 x108 Hz

λ = c/f2.87 m

1.053 x108

Hz

λ = c/f2.85 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

+ =

+ =

Faster = f or ↓ λ

Slower = ↓f or λ

v=fλ

In a vacuum v = (c) speed of light

In any other medium you have to calculate velocity

Color Wavelengths

Color R O Y G B I V

λ (m) 7.00E-7 6.50E-7 6.00E-7 5.50E-7 4.70E-7 4.30E-7 4.00E-7

Baaaaaaa!

Lambda!

B

D

C

3 Hertz

2 Hertz

A

λ

f

1 sec

1 sec

1 sec

1 sec

Mass

1

Mass

2

Mass

3

Mass

4

Peri

od (

tim

e 1

sw

ing)

Title

0.2

5 m

0.5

0 m

0.7

5 m

1.0

0 m

Peri

od (

tim

e 1

sw

ing)

sTitle

0

1.0

0 m

No breaks!

0

3

String length (m)