, Chapter 1: Introduction: Waves and Phasors
Lesson #1
Chapter — Section: Chapter 1
Topics: EM history and how it relates to other fields
Highlights:
• EM in Classical era: 1000 BC to 1900
• Examples of Modern Era Technology timelines
• Concept of “fields” (gravitational, electric, magnetic)
• Static vs. dynamic fields
• The EM Spectrum
Special Illustrations:
• Timelines from CD-ROM
Timeline for Electromagnetics in the Classical Era
ca. 900 Legend has it that while walking 1752 Benjamin Franklin
BC across a field in northern Greece, a (American) invents the
shepherd named Magnus experiences lightning rod and
a pull on the iron nails in his sandals demonstrates that
by the black rock he was standing on. lightning is electricity.
The region was later named Magnesia
and the rock became known as 1785 Charles-Augustin de
magnetite [a form of iron with Coulomb (French) demonstrates that
permanent magnetism]. the electrical force between charges is
proportional to the inverse of the
ca. 600 Greek philosopher Thales square of the distance between them.
BC describes how amber,
after being rubbed 1800 Alessandro Volta
with cat fur, can pick (Italian) develops the
up feathers [static first electric battery.
electricity].
1820 Hans Christian Oersted
ca. 1000 Magnetic compass used as (Danish) demonstrates the
a navigational device. interconnection between
electricity and magnetism
through his discovery that an electric
current in a wire causes a compass
needle to orient itself perpendicular to
the wire.
,2
Lessons #2 and 3
Chapter — Sections: 1-1 to 1-6
Topics: Waves
Highlights:
• Wave properties
• Complex numbers
• Phasors
Special Illustrations:
• CD-ROM Modules 1.1-1.9
• CD-ROM Demos 1.1-1.3
, CHAPTER 1 3
Chapter 1
Section 1-3: Traveling Waves
Problem 1.1 A 2-kHz sound wave traveling in the x-direction in air was observed to
have a differential pressure p x t 10 N/m 2 at x 0 and t 50 µs. If the reference
phase of p x t is 36 , find a complete expression for p x t . The velocity of sound
in air is 330 m/s.
Solution: The general form is given by Eq. (1.17),
2πt 2πx
p x t A cos φ0
T λ
where it is given that φ0 36 . From Eq. (1.26), T 1 f 1 2 103 0 5 ms.
From Eq. (1.27),
up 330
λ 0 165 m
f 2 103
Also, since
50 10 6
2π π rad
p x 0 t 50 µs 10 (N/m2 ) A cos 36
5 10 4 180
A cos 1 26 rad 0 31A
it follows that A 10 0 31 32 36 N/m2 . So, with t in (s) and x in (m),
t x
p x t 32 36 cos 2π 106 2π 103 36 (N/m2 )
500 165
32 36 cos 4π 103 t 12 12πx 36 (N/m2 )
Problem 1.2 For the pressure wave described in Example 1-1, plot
(a) p x t versus x at t 0,
(b) p x t versus t at x 0.
Be sure to use appropriate scales for x and t so that each of your plots covers at least
two cycles.
Solution: Refer to Fig. P1.2(a) and Fig. P1.2(b).
Lesson #1
Chapter — Section: Chapter 1
Topics: EM history and how it relates to other fields
Highlights:
• EM in Classical era: 1000 BC to 1900
• Examples of Modern Era Technology timelines
• Concept of “fields” (gravitational, electric, magnetic)
• Static vs. dynamic fields
• The EM Spectrum
Special Illustrations:
• Timelines from CD-ROM
Timeline for Electromagnetics in the Classical Era
ca. 900 Legend has it that while walking 1752 Benjamin Franklin
BC across a field in northern Greece, a (American) invents the
shepherd named Magnus experiences lightning rod and
a pull on the iron nails in his sandals demonstrates that
by the black rock he was standing on. lightning is electricity.
The region was later named Magnesia
and the rock became known as 1785 Charles-Augustin de
magnetite [a form of iron with Coulomb (French) demonstrates that
permanent magnetism]. the electrical force between charges is
proportional to the inverse of the
ca. 600 Greek philosopher Thales square of the distance between them.
BC describes how amber,
after being rubbed 1800 Alessandro Volta
with cat fur, can pick (Italian) develops the
up feathers [static first electric battery.
electricity].
1820 Hans Christian Oersted
ca. 1000 Magnetic compass used as (Danish) demonstrates the
a navigational device. interconnection between
electricity and magnetism
through his discovery that an electric
current in a wire causes a compass
needle to orient itself perpendicular to
the wire.
,2
Lessons #2 and 3
Chapter — Sections: 1-1 to 1-6
Topics: Waves
Highlights:
• Wave properties
• Complex numbers
• Phasors
Special Illustrations:
• CD-ROM Modules 1.1-1.9
• CD-ROM Demos 1.1-1.3
, CHAPTER 1 3
Chapter 1
Section 1-3: Traveling Waves
Problem 1.1 A 2-kHz sound wave traveling in the x-direction in air was observed to
have a differential pressure p x t 10 N/m 2 at x 0 and t 50 µs. If the reference
phase of p x t is 36 , find a complete expression for p x t . The velocity of sound
in air is 330 m/s.
Solution: The general form is given by Eq. (1.17),
2πt 2πx
p x t A cos φ0
T λ
where it is given that φ0 36 . From Eq. (1.26), T 1 f 1 2 103 0 5 ms.
From Eq. (1.27),
up 330
λ 0 165 m
f 2 103
Also, since
50 10 6
2π π rad
p x 0 t 50 µs 10 (N/m2 ) A cos 36
5 10 4 180
A cos 1 26 rad 0 31A
it follows that A 10 0 31 32 36 N/m2 . So, with t in (s) and x in (m),
t x
p x t 32 36 cos 2π 106 2π 103 36 (N/m2 )
500 165
32 36 cos 4π 103 t 12 12πx 36 (N/m2 )
Problem 1.2 For the pressure wave described in Example 1-1, plot
(a) p x t versus x at t 0,
(b) p x t versus t at x 0.
Be sure to use appropriate scales for x and t so that each of your plots covers at least
two cycles.
Solution: Refer to Fig. P1.2(a) and Fig. P1.2(b).
