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.

Tf 1=

Periodic Waves

λλ fT

v ==Since velocity is distance/time è

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:

Chapter 22

Electromagnetic Waves

The Nature of Electromagnetic Waves

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.

How to produce an electromagnetic wave Two straight wires connected to the terminals of an AC generator can create an electromagnetic wave.

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

The speed of an electromagnetic wave in a vacuum is: sm1000.3 8×=c

radiation field wave far from the antenna.

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:

λfc =

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.

nm 750m105.7Hz104.0

sm1000.3 714

8

=×=×

×== −

fc

λ

nm 380m108.3Hz107.9

sm1000.3 714

8

=×=×

×== −

fc

λ

red

violet

The Electromagnetic Spectrum

AM m 244Hz101230

sm1000.33

8

=×

×==

fv

λ

FM m 26.3Hz1091.9

sm1000.36

8

=×

×==

fv

λ

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.

c

c

~ 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 sm 458792299=c

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.

L

f

tpath =2Lc

T8= tpath ⇒

18 f

=2Lc

f = c16L

=3.0×108

16 3.5×104( )= 540 Hz

For observer to see light

Period of turning

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

( )( )( )sm1000.3

AmT104mNC1085.811 8

72212×=

⋅×⋅×==

−− πµε oo

c

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,

This is in excellent agreement with the experimental value.