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CHAPTER 16
16.1 TRANSVERSE WAVES
16.5 INTERFERENCE OF WAVES
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Review: Maxwell’s Equations Summary
The four fundamental equations of electromagnetism: Maxwell’s equations
Name
Gauss' law for
Equation
ර𝐸 ⋅ 𝑑 𝐴Ԧ = 𝑞enc /ε0
electricity
Gauss' law for
Relates net electric flux to net enclosed electric charge
ර𝐵 ⋅ 𝑑𝐴Ԧ = 0
magnetism
Relates net magnetic flux to net enclosed magnetic charge
Faraday’s law
𝑑Φ𝐵
ර𝐸 ⋅ 𝑑 𝑠Ԧ = −
𝑑𝑡
Ampere-Maxwell law
ර𝐵 ⋅ 𝑑𝑠Ԧ = 𝜇0 ε0
Relates induced electric field to changing magnetic flux
𝑑Φ𝐸
+ 𝜇0 𝑖enc
𝑑𝑡
Relates induced magnetic field to changing
electric flux and to current
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Electromagnetic Waves
• A changing magnetic field induces an
electric field (Faraday).
• A changing electric field induces a magnetic
field (Maxwell).
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The fields propagate as a wave at a speed
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=𝑐
𝜖0 𝜇0
𝑐 = 2.9979 × 108 m/s
Animation: https://commons.wikimedia.org/wiki/File:EMWave.gif
Author: And1mu Licensing: Creative Commons 4.0
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Electromagnetic Waves
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Electromagnetic Waves
• Predicted by Maxwell’s Laws
• AKA: light waves, radio waves, X-rays,
gamma rays, …
• For propagating waves in vacuum,
𝐸 and 𝐵 are:
• ⊥ to the direction of motion
• ⊥ to each other
• in phase (peaks at the same place)
• moving at speed 𝑐
• related in magnitude:
𝐸
=𝑐
𝐵
• (Some caveats apply for waves in materials)
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Electromagnetic Waves
•
In Maxwell’s time (the mid 1800s), the visible, infrared, and ultraviolet forms of light
were the only electromagnetic waves known.
•
Later, Heinrich Hertz discovered what we now call radio waves and verified that they
move at the same speed as visible light.
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Travelling Electromagnetic Waves
Shortwave radio region of the spectrum: an LC oscillator produces a
sinusoidal current in the antenna, which generates the wave.
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Types of Waves
Mechanical Waves: These waves require a medium (such as air, water, or a
solid) to propagate. Mechanical waves transfer energy through the motion of
particles in the medium.
Examples: water waves, sound waves, and seismic waves.
Electromagnetic waves: Electromagnetic waves do not require a medium for
propagation; they can travel through a vacuum. These waves are a combination
of electric and magnetic fields oscillating perpendicularly to each other
Examples: visible light, radio waves, microwaves, and X-rays.
Matter waves: These waves are associated with electrons, protons, and other
fundamental particles, and even atoms and molecules. Because we commonly
think of these particles as constituting matter
Examples: matter waves.
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Transverse and longitudinal Waves
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Example of Transverse Wave
A sinusoidal wave is sent along the string. A typical
string element moves up and down continuously as
the wave passes. This is transverse wave.
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Example of Longitudinal Wave
A sound wave is set up in an air- filled pipe by moving a
piston back and forth. Because the oscillations of an element
of the air (represented by the dot) are parallel to the direction
in which the wave travels, the wave is a longitudinal wave.
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Sinusoidal Wave
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Wave Parameters
Period, Wave Number, Angular
Frequency and Frequency
k=
2

( angular wave number ) .
=
2
T
f =
1 
=
T 2
( angular frequency ) .
( frequency ) .
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