The Nature of Waves
Since we will be studying electromagnetic waves, let’s review some
general features of waves:
1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.
The Nature of Waves
Longitudinal Wave - the “disturbance” caused by the wave
moves along the direction that the wave propagates,
e.g., sound waves, “compressed slinky waves”……
The Nature of Waves
Transverse Wave - the “disturbance” caused by the wave moves
perpendicular to the direction that the wave propagates,
e.g., water waves, “shaken slinky waves”, electromagnetic
waves….
Periodic Waves
Periodic waves consist of cycles or patterns that are produced over and
over again by the source.
In the figures, every segment of the slinky vibrates in a simple harmonic
motion, provided the end of the slinky is moved in a simple harmonic
motion.
Periodic Waves
In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium from
the particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is the number of cycles per time. It is related to the period
and has units of Hz, or s-1.
1
f =
T
Periodic Waves
The propagation velocity of a periodic wave is related to its frequency and
wavelength. Consider the motion of a long train as a periodic wave which
repeats itself with the passing of each identical car:
Since velocity is
distance/time
è
λ
v = = fλ
T
Chapter 22
Electromagnetic
Waves
The Nature of Electromagnetic Waves
How to produce an electromagnetic wave
Two straight wires connected to the terminals
of an AC generator can create an
electromagnetic wave.
Electric part of wave:
In each part of the drawing, the red arrow
represents E produced at point P by the
oscillating charges on the antenna at the
indicated time. The black arrows represent
E created at earlier times.
For simplicity, only the electric wave traveling
to the right is shown here.
The Nature of Electromagnetic Waves
Magnetic part of wave:
The current used to generate
the electric wave creates a
magnetic field.
Using RHR to find the direction
of B at point P for this current
direction shows that B is
perpendicular to E since E is
parallel to I.
The Nature of Electromagnetic Waves
We just showed how the electromagnetic (E&M) wave is initially generated
by the ac voltage source near the antenna (near field). As the wave
moves farther away, it propagates itself by the changing E-field producing
a B-field and the changing B-field producing an E-field (radiation field).
è E&M wave is transverse and can travel through a vacuum
radiation field wave far from the antenna.
The speed of an electromagnetic
wave in a vacuum is:
8
c = 3.00 ×10 m s
The Nature of Electromagnetic Waves
A radio wave can be detected with a receiving antenna wire
that is parallel to the electric field:
è E generates an oscillating current along the antenna wire.
The Nature of Electromagnetic Waves
With a receiving antenna in the form of a loop, the magnetic
field of a radio wave can be detected,
è  From Faraday’s law, the changing magnetic flux in the loop
will create an oscillating current in it.
The Electromagnetic Spectrum
Like all waves, electromagnetic waves have a wavelength and
frequency, related by:
c = fλ
The Electromagnetic Spectrum
Example: The Wavelength of Visible Light
Find the range in wavelengths for visible light in the frequency range
between 4.0 x 1014 Hz and 7.9 x 1014 Hz.
c 3.00 ×108 m s
−7
λ= =
=
7
.
5
×
10
m = 750 nm
14
f
4.0 ×10 Hz
red
c 3.00 ×108 m s
−7
λ= =
=
3
.
8
×
10
m = 380 nm
14
f
7.9 ×10 Hz
violet
The Electromagnetic Spectrum
Example: The Wavelength of Radio Waves
A station broadcasts AM radio waves whose frequency is 1230 x 103 Hz
and FM radio waves whose frequency is 91.9 x 106 Hz. Find the
wavelength of each type of wave.
AM
3.00 ×108 m s
λ= =
= 244 m
3
f 1230 ×10 Hz
FM
3.00 ×108 m s
λ= =
= 3.26 m
6
f
91.9 ×10 Hz
cv
cv
~ three
football fields
~ 10 ft
The Electromagnetic Spectrum
Conceptual Example: The Diffraction of AM and FM Radio Waves
Diffraction is the ability of a wave to bend around an obstacle or the
edges of an opening. Would you expect AM or FM radio waves to
bend more readily around an obstacle such as a building?
AM waves are much longer than FM waves (as seen in our example), and
waves tend to bend easier around objects (i.e. diffract) when the object’s
size is on the order of or less than the size of the wavelength. It is found
that AM waves bend easier around buildings and hills than FM waves,
which are essentially “line-of-sight.”
The Speed of Light
The speed of light
in a vacuum
c = 299 792 458 m s
Michelson device to measure the speed
of light (c. 1926). If the angular speed
of the rotating mirror is adjusted just
right, the observer can see the light
source after it has reflected from the
path shown.
From this angular speed and knowing
the distance to the fixed mirror, the
speed of light can be calculated.
Calculate the minimum frequency
the rotating mirror must turn to
measure the speed of light.
f
L
Period of turning
2L
t path =
c
T
= t path
8
1 2L
⇒
=
8f
c
For observer
to see light
c
3.0 ×108
f=
=
= 540 Hz
4
16L 16 (3.5 ×10 )
The Speed of Light
Conceptual Example: Looking Back in Time
A supernova is a violent explosion that occurs at the death of certain
stars. The figure shows a photograph of the sky before and after a
supernova. Why do astronomers say that viewing an event like this
is like looking back in time?
The Speed of Light
Maxwell’s prediction of the speed of light
Assuming that E&M waves are produced by oscillatory electric and
magnetic fields, in 1865 Maxwell predicted the speed of light using
the values known at the time for the permittivity of free space, ε0,
and the permeability of free space, µ0, as,
c=
1
=
ε o µo
1
(8.85 ×10
−12
(
))(
C 2 N ⋅ m 2 4π ×10 −7 T ⋅ m A
)
= 3.00 ×108 m s
This is in excellent agreement with the experimental value.