Unit 1 Wave Motion and Sound
Waves
Oscillatory Motion
Chapter Outline

Hooke’s Law: Stress and Strain
Explain Newton’s third law of motion with respect to stress and deformation.
Describe the restoration of force and displacement.
Calculate the energy in Hooke’s Law of deformation, and the stored energy in a
spring.

Period and Frequency in Oscillations
Observe the vibrations of a guitar string.
Determine the frequency of oscillations

Simple Harmonic Motion: A Special Periodic Motion
Describe a simple harmonic oscillator.
What do an ocean buoy, a child in a swing, the cone inside a speaker, a
guitar, atoms in a crystal, the motion of chest cavities, and the beating of
hearts all have in common? They all oscillate—-that is, they move back
and forth between two points. Many systems oscillate, and they have
certain characteristics in common. All oscillations involve force and
energy. You push a child in a swing to get the motion started. The energy
of atoms vibrating in a crystal can be increased with heat. You put energy
into a guitar string when you pluck it.
Hooke’s Law: Stress and Strain
Newton’s first law implies that an object oscillating back and forth is
experiencing forces. Without force, the object would move in a straight line
at a constant speed rather than oscillate. Consider, for example, plucking
a plastic ruler to the left as shown in Figure 1.1. The deformation of the
ruler creates a force in the opposite direction, known as a restoring force.
Once released, the restoring force causes the ruler to move back toward
its stable equilibrium position, where the net force on it is zero. However,
by the time the ruler gets there, it gains momentum and continues to move
to the right, producing the opposite deformation. It is then forced to the
left, back through equilibrium, and the process is repeated until dissipative
forces dampen the motion. These forces remove mechanical energy from
the system, gradually reducing the motion until the ruler comes to rest.
The simplest oscillations occur when the restoring force is directly
proportional to displacement. When stress and strain were covered
in Newton’s Third Law of Motion, the name was given to this relationship
between force and displacement was Hooke’s law:
The negative sign convention indicates the restoring force is in the
direction opposite to the displacement.
The force constant is related to the rigidity (or stiffness) of a system—the
larger the force constant, the greater the restoring force, and the stiffer the
system. The units of are newtons per meter (N/m).
Sample Problem #1
How Stiff Are Car Springs?
What is the force constant for the suspension system of a car that settles
1.20 cm when an 80-kg person gets in?
Strategy
Consider the car to be in its equilibrium position x=0 before the person
gets in. The car then settles down 1.20 cm, which means it is displaced to
a position x= -1.20 x 10-2 m.
At that point, the springs supply a restoring force F equal to the person’s
weight w=mg=80 kg(9.8 m/s2 )=784 N.
We take this force to be F in Hooke’s law.
Knowing F and x, we can then solve the force constant k.
Solution
Energy in Hooke’s Law of Deformation
In order to produce a deformation, work must be done. That is, a force
must be exerted through a distance, whether you pluck a guitar string or
compress a car spring. If the only result is deformation, and no work goes
into thermal, sound, or kinetic energy, then all the work is initially stored in
the deformed object as some form of potential energy.
Sample Problem #1.2
Calculating Stored Energy: A Tranquilizer Gun Spring
(a) How much energy is stored in the spring of a tranquilizer gun that has
a force constant of 50.0 N/m and is compressed 0.150 m?
(b) If you neglect friction and the mass of the spring, at what speed will a
2.00-g projectile be ejected from the gun?
Strategy for a
(a): The energy stored in the spring can be found directly from elastic
potential energy equation, because k and x are given.
Solution for a
Entering the given values for k and x yields
Strategy for b
Because there is no friction, the potential energy is converted entirely into
kinetic energy. The expression for kinetic energy can be solved for the
projectile’s speed.
Solution for b
1. Identify known quantities:
2. Solve for
Period and Frequency in Oscillations
When you pluck a guitar string, the resulting sound has a steady tone
and lasts a long time. Each successive vibration of the string takes the
same time as the previous one.
We define periodic motion to be a motion that repeats itself at regular
time intervals, such as exhibited by the guitar string or by an object on a
spring moving up and down.
The time to complete one oscillation remains constant and is called
the period.
Its units are usually seconds, but may be any convenient unit of time.
Frequency is defined to be the number of events per unit time. For
periodic motion, frequency is the number of oscillations per unit time.
The relationship between frequency and period is
The SI unit for frequency is the cycle per second, which is defined to be
a hertz (Hz):
A cycle is one complete oscillation.
Sample Problem #3
Determine the Frequency of Two Oscillations: Medical Ultrasound and the Period of
Middle C
(a) A medical imaging device produces ultrasound by oscillating with a
period of 0.400 µs. What is the frequency of this oscillation?
(b) The frequency of middle C on a typical musical instrument is 264 Hz.
What is the time for one complete oscillation?
Strategy
Both questions (a) and (b) can be answered using the relationship
between period and frequency. In question (a), the period T is given and
we are asked to find frequency f . In question (b), the frequency f is given
and we are asked to find the period T.
Solution a
Substitute 0.400 µs for T in
Discussion (a)
The frequency of sound found in (a) is much higher than the highest
frequency that humans can hear and, therefore, is called ultrasound.
Appropriate oscillations at this frequency generate ultrasound used for
noninvasive medical diagnoses, such as observations of a fetus in the
womb.
Solution b
1. Identify the known values:
The time for one complete oscillation is the period T :
v
Simple Harmonic Motion
The oscillations of a system in which the net force can be described by
Hooke’s law are of special importance, because they are very common.
They are also the simplest oscillatory systems.
Simple Harmonic Motion (SHM) is the name given to oscillatory motion for
a system where the net force can be described by Hooke’s law, and such
a system is called a simple harmonic oscillator.
If the net force can be described by Hooke’s law and there is no damping
(slowing down due to friction or other non-conservative forces), then a
simple harmonic oscillator oscillates with equal displacement on either
side of the equilibrium position, as shown for an object on a spring in the
illustration.
The maximum displacement from equilibrium is called the amplitude (A).
The units for amplitude and displacement are the same but depend on the
type of oscillation. For the object on the spring, the units of amplitude and
displacement are meters.
Two important factors do affect the period of a simple harmonic oscillator.
The period is related to how stiff the system is.


A very stiff object has a large force constant (k),
which causes the system to have a smaller period.
For example, you can adjust a diving board’s
stiffness—the stiffer it is, the faster it vibrates, and
the shorter its period.
Period also depends on the mass of the oscillating
system. The more massive the system is, the longer
the period. For example, a heavy person on a diving
board bounces up and down more slowly than a light
one.
In fact, the mass m and the force constant k are the only factors that affect
the period and frequency of SHM. To derive an equation for the period
and the frequency, we must first define and analyze the equations of
motion. Note that the force constant is sometimes referred to as the spring
constant.
Period of Simple Harmonic Oscillator
Angular frequency equation
The angular frequency depends on the force constant and the mass, and
not the amplitude, which yields to the equation for the periodic of the
motion.
and, because
the frequency of a simple harmonic oscillator is
Note that neither T nor f has any dependence on amplitude.
Sample Problem # 4
Calculate the Frequency and Period of Oscillations: Bad Shock Absorbers in a Car
Calculate the frequency and period of these oscillations for such a car if
the car’s mass (including its load) is 900 kg and the force constant (k) of
the suspension system is 6.53 x 104 N/m.
Strategy
The frequency of the car’s oscillations will be that of a simple harmonic
oscillator as given in the equation
The mass and the force constant are both given.
Solution
1. Enter the known values of k and m:
2. You could use
use the
to calculate the period, but it is simpler to
and substitute the value just found for f
1.2 Wave Motion
Wave Motion
Chapter Outline

Waves
State the characteristics of a wave.
Calculate the velocity of wave propagation

Mathematics of a wave
Calculate the velocity and acceleration of the medium

Wave Speed on Stretched String
Determine the factors that affect the speed of a wave on a string
Waves
What do we mean when we say something is a wave? The most intuitive
and easiest wave to imagine is the familiar water wave. More precisely,
a wave is a disturbance that propagates, or moves from the place it was
created. For water waves, the disturbance is in the surface of the water,
perhaps created by a rock thrown into a pond or by a swimmer splashing
the surface repeatedly. For sound waves, the disturbance is a change in
air pressure, perhaps created by the oscillating cone inside a speaker. For
earthquakes, there are several types of disturbances, including
disturbance of Earth’s surface and pressure disturbances under the
surface. Even radio waves are most easily understood using an analogy
with water waves. Visualizing water waves is useful because there is more
to it than just a mental image. Water waves exhibit characteristics
common to all waves, such as amplitude, period, frequency and energy.
All wave characteristics can be described by a small set of underlying
principles.
Waves
A wave is a disturbance that propagates, or moves from the place it was
created. There are three basic types of waves: mechanical waves,
electromagnetic waves, and matter waves.
1. Mechanical waves
These waves are most familiar because we encounter them almost
constantly; common examples include water waves, sound waves, and
seismic waves. All these waves have two central features: They are
governed by Newton’s laws, and they can exist only within a material
medium, such as water, air, and rock.
2. Electromagnetic waves
These waves are less familiar, but you use them constantly; common
examples include visible and ultraviolet light, radio and television waves,
microwaves, x rays, and radar waves. These waves require no material
medium to exist. Light waves from stars, for example, travel through the
vacuum of space to reach us. All electromagnetic waves travel through a
vacuum at the same speed c = 299 792 458 m/s.
3. Matter waves
Although these waves are commonly used in modern technology, they are
probably very unfamiliar to you. 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, such waves are called matter waves.
Much of what we discuss in this chapter applies to waves of all kinds. However, for
specific examples we shall refer to mechanical waves.
Wave Motion
Figure 2.1
Consider the simplified surface water wave that moves across the surface
of water as illustrated in Figure 2.1 above as an example of a Mechanical
Waves. Unlike complex ocean waves, in surface water waves, the
medium, in this case water, moves vertically, oscillating up and down,
whereas the disturbance of the wave moves horizontally through the
medium.
The waves cause a seagull to move up and down in simple harmonic
motion as the wave crests and troughs (peaks and valleys) pass under
the bird. The crest is the highest point of the wave, and the trough is the
lowest part of the wave.
The time for one complete oscillation of the up-and-down motion is the
wave’s period T.
The wave’s frequency is the number of waves that pass through a point
per unit time and is equal to
Wave velocity, vw define to be the speed at which the disturbance moves.
It is sometimes also called the propagation velocity or propagation speed,
because the disturbance propagates from one location to another.
The amplitude of the wave (A) is a measure of the maximum displacement
of the medium from its equilibrium position.
The water wave in the figure also has a length associated with it, called
its wavelength λ, the distance between adjacent identical parts of a wave.
(λ is the distance parallel to the direction of propagation).
The speed of propagation vw is the distance the wave travels in a given
time, which is one wavelength in the time of one period. The equation form
is,
or
This fundamental relationship holds for all types of waves.
For water waves
For sound
For visible light
Sample Problem #5
Calculate the wave velocity of the ocean wave in figure below if the
distance between wave crests is 10.0 m and the time for a sea gull to
bob up and down is 5.00 s.
Strategy
We are asked to find
and
, The given information tells us that
Therefore, we can use
Solution
1. Enter the known values into
to find the wave velocity.
Characteristics of a Wave
Transverse and Longitudinal Waves
A simple wave consists of a periodic disturbance that propagates from one
place to another. The wave in Figure 2.2a propagates in the horizontal
direction while the surface is disturbed in the vertical direction. Such a
wave is called a transverse wave or shear wave; in such a wave, the
disturbance is perpendicular to the direction of propagation. In contrast, in
a longitudinal wave or compressional wave, the disturbance is parallel to
the direction of propagation. Figure 2.2b shows an example of longitudinal
wave.
Figure 2.2
Waves may be transverse, longitudinal, or a combination of the two.
(Water waves are actually a combination of transverse and longitudinal.
The simplified water wave illustrated in Figure 2.1 shows no longitudinal
motion of the bird.) The waves on the strings of musical instruments are
transverse—so are electromagnetic waves, such as visible light.
Energy in Waves: Intensity
All waves carry energy. The energy of some waves can be
directly observed. Earthquakes can shake whole cities to
the ground, performing the work of thousands of wrecking
balls. Loud sounds pulverize nerve cells in the inner ear,
causing permanent hearing loss. Ultrasound is used for
deep-heat treatment of muscle strains. A laser beam can
burn away a malignancy. Water waves chew up beaches.
The amount of energy in a wave is related to its amplitude. Largeamplitude earthquakes produce large ground displacements. Loud
sounds have higher pressure amplitudes and come from larger-amplitude
source vibrations than soft sounds. Large ocean breakers churn up the
shore more than small ones. More quantitatively, a wave is a displacement
that is resisted by a restoring force.
The larger the displacement x, the larger the force
needed to
create it. Because work W is related to force multiplied by distance (Fx)
and energy is put into the wave by the work done to create it, the energy
in a wave is related to amplitude. In fact, a wave’s energy is directly
proportional to its amplitude squared because
The energy effects of a wave depend on time as well as amplitude. For
example, the longer deep-heat ultrasound is applied, the more energy it
transfers. Waves can also be concentrated or spread out. Sunlight, for
example, can be focused to burn wood. Earthquakes spread out, so they
do less damage the farther they get from the source. In both cases,
changing the area the waves cover has important effects. All these
pertinent factors are included in the definition of intensity I as power per
unit area:
Sample Problem #6
Calculating intensity and power: How much energy is in a ray of sunlight?
The average intensity of sunlight on Earth’s surface is about
Calculate the amount of energy that falls on a solar collector having an
area of
in 4.00 h.
Strategy a
Because power is energy per unit time or
intensity can be written as
for E with the given information.
Solution
, the definition of
and this equation can be solved
Sample Problem #6
A transverse mechanical wave (Graph 1)propagates in the positive xdirection through a spring with a constant wave speed, and the medium
oscillates between +A and -A around an equilibrium position.
Graph 1
The graph in Figure 2.3 shows the height of the spring (y) versus the
position (x), where the x-axis points in the direction of propagation. The
figure shows the height of the spring versus the x-position at t = 0.00 s
as a dotted line and the wave at t = 3.00 s as a solid line.
(a) Determine the wavelength and amplitude of the wave.
(b) Find the propagation velocity of the wave.
(c) Calculate the period and frequency of the wave.
Figure 2.3
Solution:
a. Read the wavelength from the graph below, looking at the purple
arrow in below. Read the amplitude by looking at the green arrow. The
wavelength is λ = 8.00 cm and the amplitude is A = 6.00 cm.
b. The distance the wave traveled from time t = 0.00 s to time t = 3.00 s
can be seen in the graph. Consider the red arrow, which shows the
distance the crest has moved in 3 s. The distance is 8.00 cm - 2.00 cm
= 6.00 cm. The velocity is
c. The period is
Frequency is
Mathematics of Waves
The wave on the string travels in the positive x-direction with a constant
velocity v, and moves a distance vt in a time t. The wave function is
defined by
It is often convenient to rewrite this wave function in a more compact
form.
The value
is defined as the wave number. The symbol for the wave
number is k and has units of inverse meters, m-1 :
Recall that angular frequency is equated to
The second term of the wave function becomes
The wave function for a simple harmonic wave on a string reduces to
where
The minus sign is for waves moving in the positive x-direction, and the
plus sign is for waves moving in the negative x-direction.
The velocity of the wave is equal to
Sample Problem #7
Characteristics of a Traveling Wave on a String
A transverse wave on a taut string is modeled with the wave function
Find the amplitude, wavelength, period, and speed of the wave.
Solution:
1. Amplitude =0.2 m
K=6.28 m-1
2. The wave number can be used to find the wavelength
3. The period of the wave can be found using the angular frequency:
4. The speed of the wave can be found using the wave number and the
angular frequency. The direction of the wave can be determined by
considering the sign of
. A negative sign suggests that the wave
is moving in the positive x-direction:
Wave Speed on a Stretched String
The speed of a wave depends on the characteristics of the medium. The
speed of the waves on the strings, and the wavelength, determine the
frequency of the sound produced. The speed of the waves on the strings,
and the wavelength, determine the frequency of the sound produced.
They have different linear densities, where the linear density is defined as
the mass per length,
Example
If the string has a length of 2.00 m and a mass of 0.06 kg. What is its
linear density?
Wave Speed on a String under Tension
The speed of a pulse or wave on a string under tension can be found
with the equation
Sample Problem #8
The Wave Speed of a Guitar Spring
On a six-string guitar, the high E string has a linear density
of
and the low E string has a linear density
of
(a) If the high E string is plucked, producing a wave in the string, what is
the speed of the wave if the tension of the string is 56.40 N?
(b) Calculate the tension of the low E string needed for the same wave
speed.
Solution:
a.
b.
1.3 Sound
Sound
Outline

Sound
• Difference between sound and hearing
• Sound as a wave

Speed of Sound
• The relationship between wavelength and frequency of sound
• The equation for the speed of sound in air

The Doppler Effect
• The change in observed frequency as a moving source of sound approaches
or departs from a stationary observer
• The change in observed frequency as an observer moves toward or away
from a stationary source of sound
Sound is an example of a mechanical wave, specifically, a
pressure wave: Sound waves travel through the air and
other media as oscillations of molecules. Normal human
hearing encompasses an impressive range of frequencies
from 20 Hz to 20 kHz. Sounds below 20 Hz are called
infrasound, whereas those above 20 kHz are called
ultrasound
Sound Waves
The physical phenomenon of sound is a disturbance of matter that is
transmitted from its source outward. Hearing is the perception of sound,
just as seeing is the perception of visible light.
On the atomic scale, sound is a disturbance of atoms that is far more
ordered than their thermal motions. In many instances, sound is a periodic
wave, and the atoms undergo simple harmonic motion. Thus, sound
waves can induce oscillations and resonance effects.
A speaker produces a sound wave by oscillating a cone, causing
vibrations of air molecules. In Figure below, a speaker vibrates at a
constant frequency and amplitude, producing vibrations in the surrounding
air molecules.
As the speaker oscillates back and forth, it transfers energy to the air,
mostly as thermal energy. But a small part of the speaker’s energy goes
into compressing and expanding the surrounding air, creating slightly
higher and lower local pressures.
These compressions (high-pressure regions) and rarefactions (lowpressure regions) move out as longitudinal pressure waves having the
same frequency as the speaker—they are the disturbance that is a sound
wave. (Sound waves in air and most fluids are longitudinal, because fluids
have almost no shear strength. In solids, sound waves can be both
transverse and longitudinal.)
Models Describing Sound
Sound can be modeled as a pressure wave by considering the change in
pressure from average pressure,
This equation is similar to the periodic wave equations seen in Waves,
Sound waves can also be modeled in terms of the displacement of the
air molecules. The displacement of the air molecules can be modeled
using a cosine function:
In this equation, s is the displacement and smax is the maximum
displacement.
Wavelength, frequency, amplitude, and speed of propagation are important
characteristics for sound, as they are for all waves.
Speed of Sound
Sound, like all waves, travels at a certain speed and has the properties of
frequency and wavelength. You can observe direct evidence of the speed
of sound while watching a firework display. You see the flash of an
explosion well before you hear its sound and possibly feel the pressure
wave, implying both that sound travels at a finite speed and that it is much
slower than light.
The difference between the speed of light and the speed of sound can
also be experienced during an electrical storm. The flash of lighting is
often seen before the clap of thunder. You may have heard that if you
count the number of seconds between the flash and the sound, you can
estimate the distance to the source. Every five seconds converts to about
one mile. The velocity of any wave is related to its frequency and
wavelength by
where v is the speed of the wave, f is its frequency, and λ is its wavelength.
Speed of Sound in Various Media
In a fluid, the speed of sound depends on the bulk modulus and the
density
The speed of sound in a solid the depends on the Young’s modulus of
the medium and the density
The equation for the speed of sound is
where γ is the adiabatic index, R = 8.31 J/mol · K is the gas constant,
TK is the absolute temperature in kelvins, and M is the molecular mass.
For air at sea level, the speed of sound is given by
Sample Problem #7
Calculating Wavelengths
Calculate the wavelengths of sounds at the extremes of the audible range,
20
and
20,000
Hz,
in
30.0°C
air.
(Assume that the frequency values are accurate to two significant figures.)
Strategy
To find wavelength from frequency, we can use v = f λ.
Solution
1. Identify knowns. The value for v is given by
2. Convert the temperature into kelvins and then enter the temperature
into the equation
3. Solve the relationship between speed and wavelength for λ:
4. Enter the speed and the minimum frequency to give the maximum
wavelength:
5. Enter the speed and the maximum frequency to give the minimum
wavelength:
The speed of sound can change when sound travels from one medium to another, but
the frequency usually remains the same. This is similar to the frequency of a wave on
a string being equal to the frequency of the force oscillating the string. If v changes and
f remain the same, then the wavelength λ must change. That is, because v = f λ, the
higher the speed of a sound, the greater its wavelength for a given frequency.
Sound Intensity and Sound Level
Intensity is defined to be the power per unit area carried by a wave. Power
is the rate at which energy is transferred by the wave. In equation
form intensity I
The intensity of a sound wave is related to its amplitude squared by the following
relationship:
Sound intensity levels are quoted in decibels (dB) much more often than
sound intensities in watts per meter squared. Decibels are the unit of
choice in the scientific literature as well as in the popular media.
The reasons for this choice of units are related to how we perceive
sounds. How our ears perceive sound can be more accurately described
by the logarithm of the intensity rather than directly to the intensity.
The sound intensity level β in decibels of a sound having an intensity I in
watts per meter squared is defined to be
I0 is the lowest or threshold intensity of sound a person with normal
hearing can perceive at a frequency of 1000 Hz.
Sound intensity level is not the same as intensity because β is defined in
terms of a ratio, it is a unitless quantity telling you the level of the sound
relative to a fixed standard
,in this case)
The units of decibels (dB) are used to indicate this ratio is multiplied by 10
in its definition. The bel, upon which the decibel is based, is named for
Alexander Graham Bell, the inventor of the telephone.
Sample Problem #8
Calculating Sound Intensity Levels: Sound Waves
Calculate the sound intensity level in decibels for a sound wave traveling
in air 0^° C at and having a pressure amplitude of 0.656 Pa.
Strategy
We are given p, so we can calculate I using the equation
Using I, we can calculate β straight from its definition in
Solution
(1) Identify knowns:
Sound
travels
at
331
m/s
in
air
at
0°
Air has a density of 1.29 kg/m3 at atmospheric pressure and 0° C
(2) Enter these values and the pressure amplitude into
Sample Problem #9
C
.
Change Intensity Levels of a Sound: What Happens to the Decibel Level?
Show that if one sound is twice as intense as another, it has a sound level
about 3 dB higher.
Strategy
You are given that the ratio of two intensities is 2 to 1, and are then asked
to find the difference in their sound levels in decibels. You can solve this
problem using of the properties of logarithms.
Solution
(1)
Identify
The ratio of the two intensities is 2 to 1, or:
knowns:
We wish to show that the difference in sound levels is about 3 dB That is,
we want to show:
Note that:
(2) Use the definition β of to get:
Thus,
Doppler Effect
The characteristic sound of a motorcycle buzzing by is an example of the
Doppler effect. Specifically, if you are standing on a street corner and
observe an ambulance with a siren sounding passing at a constant speed,
you notice two characteristic changes in the sound of the siren.
First, the sound increases in loudness as the ambulance approaches and
decreases in loudness as it moves away, which is expected. But in
addition, the high-pitched siren shifts dramatically to a lower-pitched
sound. As the ambulance passes, the frequency of the sound heard by a
stationary observer changes from a constant high frequency to a constant
lower frequency, even though the siren is producing a constant source
frequency. The closer the ambulance brushes by, the more abrupt the
shift. Also, the faster the ambulance moves, the greater the shift. We also
hear this characteristic shift in frequency for passing cars, airplanes, and
trains.
The Doppler effect is an alteration in the observed frequency of a sound
due to motion of either the source or the observer. Although less familiar,
this effect is easily noticed for a stationary source and moving observer.
For example, if you ride a train past a stationary warning horn, you will
hear the horn’s frequency shift from high to low as you pass by. The actual
change in frequency due to relative motion of source and observer is
called a Doppler shift.
The Doppler effect and Doppler shift are named for the Austrian physicist
and mathematician Christian Johann Doppler (1803–1853), who did
experiments with both moving sources and moving observers.
Doppler Effect
The Doppler effect occurs not only for sound, but for any wave when there
is relative motion between the observer and the source. Doppler shifts
occur in the frequency of sound, light, and water waves, for example.
Doppler shifts can be used to determine velocity, such as when ultrasound
is reflected from blood in a medical diagnostic. he relative velocities of
stars and galaxies is determined by the shift in the frequencies of light
received from them and has implied much about the origins of the
universe.
Modern physics has been profoundly affected by observations of Doppler
shifts.
General Equation
The choice of plus or minus signs (sign convention) is set by this rule:
When the motion of detector or source is toward the other, the sign on its
speed must give an upward shift in frequency. When the motion of
detector or source is away from the other, the sign on its speed must give
a downward shift in frequency.
*In short, toward means shift up and away means shift down.
Here are some examples of the rule. If the detector moves toward the
source, use the plus sign in the numerator of the general equation to get
a shift up in the frequency. If it moves away, use the minus sign in the
numerator to get a shift down. If it is stationary, substitute 0 for vD. If the
source moves toward the detector, use the minus sign in the denominator
of the general equation to get a shift up in the frequency. If it moves away,
use the plus sign in the denominator to get a shift down. If the source is
stationary, substitute 0 for vs.
Sample Problem 10
Calculating a Doppler Shift
Suppose a train that has a 150-Hz horn is moving at 35.0 m/s in still air
on a day when the speed of sound is 340 m/s.
(a) What frequencies are observed by a stationary person at the side of
the tracks as the train approaches and after it passes?
(b) What frequency is observed by the train’s engineer traveling on the
train?
Strategy
To find the observed frequency in (a), we must use
because the source is moving. The minus sign is used for the
approaching train, and the plus sign for the receding train.
Solution
a. Enter known values into
Calculate the frequency observed by a stationary person as the train
approaches:
Use the same equation with the plus sign to find the frequency heard by
a stationary person as the train recedes:
Calculate the second frequency
Sample Problem 11
Double Doppler shift in the echoes used by bats
Bats navigate and search out prey by emitting, and then detecting
reflections of, ultrasonic waves, which are sound waves with frequencies
greater than can be heard by a human. Suppose a bat emits ultrasound
at frequency
while flying with velocity
it chases a moth that flies with velocity
frequency
does the moth detect? What frequency
detect in the returning echo from the moth?
as
.What
does the bat
Given:
Solution
Detection by moth
Since the moth is moving away from the bat the sign convention that will
be use is in negative sign
Detection of echo by bat
Since the bat is moving towards the moth sign convention that will be
use is in positive sign
Summary
Sound Waves
• Sound is a disturbance of matter (a pressure wave) that is transmitted
from its source outward. Hearing is the perception of sound.
• Sound can be modeled in terms of pressure or in terms of
displacement of molecules.
• The human ear is sensitive to frequencies between 20 Hz and 20 kHz.
Speed of Sound
• The speed of sound depends on the medium and the state of the
medium.
• In a fluid, because the absence of shear forces, sound waves are
longitudinal. A solid can support both longitudinal and transverse sound
waves.
• In air, the speed of sound is related to air temperature T by
• v is the same for all frequencies and wavelengths of sound in air.
The Doppler Effect
• The Doppler effect is an alteration in the observed frequency of a
sound due to motion of either the source or the observer.
• The actual change in frequency is called the Doppler shifts
2.1 Light Waves
Light Waves
Light reflects in the same manner that any wave would reflect. Light
refracts in the same manner that any wave would refract. Light diffracts in
the same manner that any wave would diffract.
Light undergoes interference in the same manner that any wave would
interfere. And light exhibits the Doppler effect just as any wave would
exhibit the Doppler effect. Light behaves in a way that is consistent with
our conceptual and mathematical understanding of waves. Since light
behaves like a wave, one would have good reason to believe that it might
be a wave.
The speed of light, although quite fast, is not infinite. The speed of light in
a vacuum is expressed as
Light travels in a vacuum at a constant speed, and this speed is
considered a universal constant. In a vacuum, light will travel in a straight
line at fixed speed, carrying energy from one place to another.
Two key properties of light interacting with a medium are:
1. It can be deflected upon passing from one medium to another
(refraction).
2. It can be bounced off a surface (reflection).
The field of detection and measurement of light energy is called
radiometry. It uses a standardized system for characterizing radiant
energy.
Wave Model
The particle-like model of light describes large-scale effects such as light
passing through lenses or bouncing off mirrors. However, a wavelike
model must be used to describe fine-scale effects such as interference
and diffraction that occur when light passes through small openings or by
sharp edges. The propagation of light or electromagnetic energy through
space can be described in terms of a traveling wave motion.
The wave moves energy—without moving mass—from one place to
another at a speed independent of its intensity or wavelength. This wave
nature of light is the basis of physical optics and describes the interaction
of light with media. Many of these processes require calculus and
quantum theory to describe them rigorously.
Characteristics of light waves
Figure 1-2 One Dimensional representation of the electromagnetic wave
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The maximum value of the wave displacement is called the
amplitude (A) of the wave.
The cycle starts at zero and repeats after a distance. This distance
is called the wavelength (λ). Light can have different wavelengths,
such as the blue light and red light shown in Figure 1-2.
The inverse of the wavelength (1/λ) is the wave number (ν), which is
expressed in m–1.
The wave propagates at a wave speed (v). This wave speed in a
vacuum is equal to c, and is less than c in a medium.
At a stationary point along the wave, the wave passes by in a
repeating cycle. The time to complete one cycle is called the cycle
time or period (T).

Another important measure of a wave is its frequency (f). It is
measured as the number of waves that pass a given point in one
second. The unit for frequency is cycles per second, also called
hertz (Hz). As you can see, the frequency and the period are
reciprocals of one another.
Sample Problem
What is the frequency green light that has wavelength of 5.5 x 10-7 m-1?
Solution:
v=λf
f=v/λ=3.0x10^8m/s/5.5x10−7m−1=5.5x10^14Hz
Concepts of Light Waves
Light waves are complex. They are not one-dimensional waves but rather
are composed of mutually perpendicular electric and magnetic fields with
wave motion at right angles to both fields, as illustrated in Figure 1-4. The
wave carries light energy with it. The amount of energy that flows per
second across a unit area perpendicular to the direction of travel is called
the irradiance (flux density) of the wave.
Figure 1.4 Electric and magnetic fields in a light wave.
Electromagnetic waves share six properties
with all forms of wave motion:
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
Polarization
Superposition
Reflection
Refraction
Diffraction
Interference
Polarization
Polarization arises from the direction of the E-field vector with respect to
the direction of the light’s propagation. Since a light wave’s electric field
vibrates in a direction perpendicular to its propagation motion, it is called
a transverse wave and is polarizable. A sound wave, by contrast, vibrates
back and forth along its propagation direction and thus is not polarizable.
Light is unpolarized if it is composed of vibrations in many different
directions, with no preferred orientation. Many light sources (e.g.,
incandescent bulbs, arc lamps, the sun) produce unpolarized light.
The intensity of light passing through a linear polarizer can be calculated
using Equation
where
The angle of the E-field with respect to the transmission axis is defined
as θ.
Sample Problem
Given horizontally polarized light, what would be the ratio of the light
intensity output to the light intensity input for θ = 0°, 45°, and 90°?
Huygens’ Principle
In the seventeenth century, Christian Huygens proposed a principle that
can be used to predict where a given wave front will be at any time in the
future if you know the current location. His principle assumes that each
point along a wave front can be considered a point source for production
of secondary spherical wavelets. After a period of time, the new position
of the wave front will be the surface tangent to these secondary wavelets.
Huygens’ principle is illustrated in Figure 1-6, for five point sources on a
wave front.
Figure 1.6 Using Hygens' principle to establish new wave fronts
Superposition
For many kinds of waves, including electromagnetic, two or more waves
can traverse the same space at the same time independently of one
another. This means that the electric field at any point in space is simply
the vector sum of the electric fields that the individual waves alone
produce at the point. This is the superposition principle. Both the electric
and magnetic fields of an electromagnetic wave satisfy the superposition
principle. Thus, given multiple waves, the field at any given point can be
calculated by summing each of the individual wave vectors.
Figure 1.7 Using the principle of superposition to add individual waves.
When two or more waves are superimposed, the resulting physical effect
is called interference. Suppose two waves, y1 and y2, have nearly the
same wavelength and phase (i.e., the maxima occur at nearly the same
time and place).
Superposition of these waves results in a wave (y1 + y2) of almost twice
the amplitude of the individual waves. See Figure 1-7a. This is called
constructive interference. If the maximum of one wave is near the
minimum of the other wave, the resultant (y1 + y2) has almost no
amplitude, as shown in Figure 1-7b. This is called destructive interference.
Reflection
When a ray of light reflects off a surface (such as a mirror), its new
direction depends on only the angle of incidence. The law of reflection
states that the angle of incidence on a reflecting basic surface is equal to
the angle of reflection.
Figure 1.8
Refraction
When a ray of light passes from one medium to another, it changes
direction (bends) at the interface because of the difference in speed of the
wave in the media. The ratio of this speed difference is called the index of
refraction (n). The ratio of the indices of refraction and the direction of the
two rays of light for the two media are expressed in Snell’s law as shown
figure 1.9
where n1 and n2 are the indices of refraction for the two media θ is the
angle of incidence
θ is the angle of incidence
φ is the angle of refraction
Figure 1.9 Refraction and Snell's law
Diffraction
Conclusive evidence of the correctness of a wave model came with the
explanation of observed diffraction and interference. When light passes
an obstacle, the shadow is not precise and sharp as geometrical ray
theory would predict, but rather diffracted a little into the dark region
behind the obstacle, thus giving the shadow a fuzzy edge. This property
of light that causes it to spread out as it travels by sharp edges or through
tiny holes can be explained by light having wavelike properties. Diffraction
is predicted from Huygens’ principle. In Figure 1-10, a wave is incident on
a barrier from the left. The barrier has a slit. Every point on the incident
wave front that arrives at the slit can be viewed as the site of an expanding
spherical wavelet. For apertures that are small compared to the
wavelength, the aperture becomes like a source and spherical waves
result. As the slit width d increases, the diffracted wave becomes more
and more like the incident plane wave except for the edges at the shadow.
Figure 1.10 Diffraction of waves through slits of differing size
Interference
The first definitive demonstration of the wavelike nature of light was the
classical two-slit experiment performed by Thomas Young in 1801. The
two slits are very small compared to their separation distance. Thus, each
slit produces diffracted spherical waves that overlap as they expand into
the space to the right of the barrier. When they overlap, they interfere with
each other, producing regions of mutually reinforcing waves. These
appear on the screen as regions of maximum intensity. Between adjacent
maxima is a region of minimum intensity. See Figure 1-11. The resulting
pattern on the screen shows where constructive interference occurs
(maxima, labeled B) and where destructive interference occurs (minima,
labeled D). The experimental layout shown in Figure 1-10 can be used in
practice to measure the wavelength of light.
Figure 1.11 Classic Double-slit experiment
Interactions of Light with Matter
When light travels through a medium, it interacts with the medium. The
important interactions are absorption and scattering.
Absorption
Absorption is a transfer of energy from the electromagnetic wave to the
atoms or molecules of the medium. Energy transferred to an atom can
excite electrons to higher energy states. Energy transferred to a molecule
can excite vibrations or rotations. The wavelengths of light that can excite
these energy states depend on the energy-level structures and therefore
on the types of atoms and molecules contained in the medium. The
spectrum of the light after passing through a medium appears to have
certain wavelengths removed because they have been absorbed. This is
called an absorption spectrum. Selective absorption is also the basis for
objects having color. A red apple is red because it absorbs the other colors
of the visible spectrum and reflects only red light.
Scattering
Scattering is the redirection of light caused by the light’s interaction with
matter. The scattered electromagnetic radiation may have the same or
longer wavelength (lower energy) as the incident radiation, and it may
have a different polarization. If the dimensions of the scatterer are much
smaller than the wavelength of light, like a molecule, for example, the
scatterer can absorb the incident light and quickly reemit the light in a
different direction. If the reemitted light has the same wavelength as the
incident light, the process is called Rayleigh scattering. If the reemitted
light has a longer wavelength, the molecule is left in an excited state, and
the process is called Raman scattering. In Raman scattering, secondary
photons of longer wavelength are emitted when the molecule returns to
the ground state.
2.2 Electromagnetic Waves
Electromagnetic Waves
Electromagnetic waves consist of oscillating electric and magnetic fields
and propagate at the speed of light. They were predicted by Maxwell,
who also showed that light is energy emitted by accelerating electric
charges, usually electrons.
This energy travels in a wave that is partially electric and partially
magnetic these are electromagnetic waves.
Unlike sound waves electromagnetic waves do not require a medium.
i.e. They can travel through space
Electrons in materials are vibrated and emit energy in the form of
photons, which propagate across the universe.
Photons have no mass, but are pure energy. Electromagnetic Waves are
waves that are made up of these “photons”. When these photons come
in contact with boundaries, E-M waves interact like other waves would.
Electromagnetic waves are everywhere.
e.g

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Radios
TVs
Microwaves
Light (Visible/UV/Infrared)
Radiation
Lasers
X-Rays
Misconception Alert: Sound Waves vs. Radio Waves
Many people confuse sound waves with radio waves, one type of
electromagnetic (EM) wave. However, sound and radio waves are
completely different phenomena. Sound creates pressure variations
(waves) in matter, such as air or water, or your eardrum. Conversely, radio
waves are electromagnetic waves, like visible light, infrared, ultraviolet, Xrays, and gamma rays. EM waves don’t need a medium in which to
propagate; they can travel through a vacuum, such as outer space.
A radio works because sound waves played by the D.J. at the radio station
are converted into electromagnetic waves, then encoded and transmitted
in the radio-frequency range. The radio in your car receives the radio
waves, decodes the information, and uses a speaker to change it back
into a sound wave, bringing sweet music to your ears.
Maxwell’s Equations: Electromagnetic Waves Predicted and Observed
1. Electric field lines originate on positive charges and terminate on
negative charges. The electric field is defined as the force per unit charge
on a test charge, and the strength of the force is related to the electric
constant, also known as the permittivity of free space. From Maxwell’s first
equation we obtain a special form of Coulomb’s law known as Gauss’s
law for electricity.
2. Magnetic field lines are continuous, having no beginning or end. No
magnetic monopoles are known to exist. The strength of the magnetic
force is related to the magnetic constant μ0, also known as the permeability
of free space. This second of Maxwell’s equations is known as Gauss’s
law for magnetism.
3. A changing magnetic field induces an electromotive force (EMF) and,
hence, an electric field. The direction of the EMF opposes the change.
This third of Maxwell’s equations is Faraday’s law of induction, and
includes Lenz’s law.
4. Magnetic fields are generated by moving charges or by changing
electric fields. Tis fourth of Maxwell’s equations encompasses Ampere’s
law and adds another source of magnetism—changing electric fields.
Making Connections: Unification of Forces
Maxwell’s complete and symmetric theory showed that electric and
magnetic forces are not separate, but different manifestations of the same
thing—the electromagnetic force. This classical unification of forces is one
motivation for current attempts to unify the four basic forces in nature—
the gravitational, electrical, strong, and weak nuclear forces.
Maxwell calculated that electromagnetic waves would propagate at a
speed given by the equation
Where
When the values for and are entered into the equation for, we find that
which is the speed of light. In fact, Maxwell concluded that light is an
electromagnetic wave having such wavelengths that it can be detected by
the eye.
All electromagnetic waves, including visible light, have the same speed c
in vacuum
Production of Electromagnetic Waves
In keeping with these features, we can assume that the electromagnetic
wave is traveling toward P in the positive direction of an x axis, that the
electric field is oscillating parallel to the y axis, and that the magnetic field
is then oscillating parallel to the z axis (using a right-handed coordinate
system, of course). Then, we can write the electric and magnetic fields as
sinusoidal functions of position x (along the path of the wave) and time t:
where
Relating E-Field and B-Field Strengths
There is a relationship between the E- and B-field strengths in an
electromagnetic wave. This can be understood by again considering the
antenna just described. The stronger the E-field created by a separation
of charge, the greater the current and, hence, the greater the B-field
created.
Since current is directly proportional to voltage (Ohm’s law) and voltage is
directly proportional to -field strength, the two should be directly
proportional. It can be shown that the magnitudes of the fields do have a
constant ratio, equal to the speed of light. That is,
is the ratio of E-field strength to B-field strength in any electromagnetic
wave. This is true at all times and at all locations in space. A simple and
elegant result.
Sample Problem
Calculating B-Field Strength in an Electromagnetic Wave
What is the maximum strength of the B-field in an electromagnetic wave
that has a maximum E-field strength of 1000 V/m?
Solution:
Electromagnetic Spectrum
A brief overview of the production and utilization of electromagnetic
waves is found below
Electromagnetic Spectrum
Connections: Waves
There are many types of waves, such as water waves and even
earthquakes. Among the many shared attributes of waves are propagation
speed, frequency, and wavelength. These are always related by the
expression. This module concentrates on EM waves, but other modules
contain examples of all of these characteristics for sound waves and
submicroscopic particles.
Electromagnetic Spectrum: Rules of Thumb
Tree rules that apply to electromagnetic waves in general are as follows:
• High-frequency electromagnetic waves are more energetic and are more
able
to
penetrate
than
low-frequency
waves.
• High-frequency electromagnetic waves can carry more information per
unit
time
than
low-frequency
waves.
• The shorter the wavelength of any electromagnetic wave probing a
material, the smaller the detail it is possible to resolve.
Note that there are exceptions to these rules of thumb.
As noted before, an electromagnetic wave has a frequency and a
wavelength associated with it and travels at the speed of light, or c. The
relationship among these wave characteristics can be described by ,
where is the propagation speed of the wave, is the frequency, and is the
wavelength. Here vw=c , so that for all electromagnetic waves,
Thus, for all electromagnetic waves, the greater the frequency, the
smaller the wavelength.
The electromagnetic spectrum is separated into many categories and
subcategories, based on the frequency and wavelength, source, and uses
of the electromagnetic waves.
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Any electromagnetic wave produced by currents in wires is classified
as a radio wave, the lowest frequency electromagnetic waves.
Radio waves are divided into many types, depending on their
applications, ranging up to microwaves at their highest frequencies.
Infrared radiation lies below visible light in frequency and is
produced by thermal motion and the vibration and rotation of atoms
and molecules. Infrared’s lower frequencies overlap with the
highest-frequency microwaves.
Visible light is largely produced by electronic transitions in atoms and
molecules, and is defined as being detectable by the human eye.
Its colors vary with frequency, from red at the lowest to violet at the
highest.
Ultraviolet radiation starts with frequencies just above violet in the
visible range and is produced primarily by electronic transitions in
atoms and molecules.
X-rays are created in high-voltage discharges and by electron
bombardment of metal targets. Their lowest frequencies overlap
the ultraviolet range but extend to much higher values, overlapping
at the high end with gamma rays.
Gamma rays are nuclear in origin and are defined to include the
highest-frequency electromagnetic radiation of any type.
Sample Problem
Calculating Wavelengths of Radio Waves
Calculate the wavelengths of a 1530-kHz AM radio signal, a 105.1-MHz
FM radio signal, and a 1.90-GHz cell phone signal.
Solution
a. For the f=1530 kHz AM radio signal, then
b. For the f=105.1 MHz FM radio signal,
(c) And for the f=1.90 GHz cell phone,
These wavelengths are consistent with the spectrum
Energy Carried by Electromagnetic Waves
Electromagnetic waves can bring energy into a system by virtue of their
electric and magnetic fields. These fields can exert forces and move
charges in the system and, thus, do work on them. If the frequency of
the electromagnetic wave is the same as the natural frequencies of the
system (such as microwaves at the resonant frequency of water
molecules), the transfer of energy is much more efficient.
The energy carried by any wave is proportional to its amplitude squared.
For electromagnetic waves, this means intensity can be expressed as
where
This can also be expressed in terms of the maximum magnetic field
strength B0 as
and in terms of both electric and magnetic fields as
The three expressions for Iave are all equivalent. Since these equations
are based on the assumption that the electromagnetic waves are
sinusoidal, peak intensity is twice the average; that is,
Sample Problem
Calculate Microwave Intensities and Fields
On its highest power setting, a certain microwave oven projects 1.00 kW
of microwaves onto a 30.0 by 40.0 cm area.
(a) What is the intensity in
(b) Calculate the peak electric field strength E0 in these waves.
(c) What is the peak magnetic field strength B0?
Solution
(a)
Note that the peak intensity is twice the average:
b.
c.
2.3 Illumination
Luminous Intensity and Luminous Flux
The brightness of a light source is called luminous intensity I, whose unit
is the candela (cd). The intensity of a light source is sometimes referred
to as its candlepower.
The amount of visible light that falls on a given surface is called luminous
flux F, whose unit is the lumen (lm). One lumen is equal to the luminous
flux which falls on each 1 m2 of a sphere 1 m in radius when a 1-cd
isotropic light source (one that radiates equally in all directions) is at the
center of the sphere. Since the surface area of a sphere of radius r is
4πr2, a sphere whose radius is 1 m has 4πr2, and the total luminous flux
emitted by a 1-cd source is therefore 4π lm. Thus, the luminous flux
emitted by an isotropic light source of intensity I is given by
The above formula does not apply to a light source that radiates different
fluxes in different directions. In such a situation, the concept of solid angle
is needed. A solid angle is the counterpart in three dimensions of an
ordinary angle in two dimensions. The solid angle Ω (Greek capital letter
omega) subtended by area A on the surface of a sphere of radius r is given
by
The unit of solid angle is the steradian (sr), see figure below. Like the
degree and the radian, the steradian is a dimensionless ratio that
disappears in calculation.
The general definition of luminous flux is
Since the total area of a sphere is 4π,the total solid angle it subtends
is
This definition of F thus gives
isotropic source.
for the total flux emitted by an
Luminous Efficiency
The luminous efficiency of a light source is the amount of luminous flux it
radiates per watt of input power. The luminous efficiency of ordinary
tungsten-filament lamps increases with their power, because the higher
the power of such a lamp, the greater its temperature and the more of its
radiation is in the visible part of the spectrum. The efficiencies of such
lamps range from about 8 lm/W for a 10-W lamp to 22 lm/W for a 1000-W
lamp. Fluorescent lamps have efficiencies from 40 to 75 lm/W.
Sample Problem
What solid angle subtended at the center of a sphere by an area of
1.6m2? The radius of the sphere is 5m.
Solution
Illumination
The illumination (or illuminance) E of a surface is the luminous flux per
unit area that reaches the surface:
In SI, the unit of illumination is the lumen per square meter, or lux (lx); in
British system, it is lumen per square foot, or footcandle (fc)
The illumination on a surface a distance R away from an isotropic source
of light of intensity I is
Where
Thus, the illumination from such a source varies inversely as R2, just as
in the case of sound waves; doubling the distance means, reducing the
illumination to ¼ its former value. For light perpendicularly incident on a
surface, θ=0 and cosaθ=1 , so in this situation,
Sample Problem
A 10-W fluorescent lamp has a luminous intensity of 35 cd. Find
(a) the luminous flux it emits and
(b) its luminous efficiency.
Solution
a.
b.
2.4 Color
Visible Light

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Visible light is a form of electromagnetic (EM) radiation, as are
radio waves, infrared radiation, ultraviolet radiation, X-rays and
microwaves. Generally, visible light is defined as the wavelengths
that are visible to most human eyes.
Visible light waves are the only electromagnetic waves we can see.
We see these waves as the colors of the rainbow. Each color has
a different wavelength. Red has the longest wavelength and violet
has the shortest wavelength. When all the waves are seen
together, they make white light.
EM radiation is transmitted in waves or particles at different
wavelengths and frequencies. This broad range of wavelengths is
known as the electromagnetic spectrum. That spectrum is
typically divided into seven regions in order of decreasing
wavelength and increasing energy and frequency. The common
designations are radio waves, microwaves, infrared (IR), visible
light, ultraviolet (UV), X-rays and gamma-rays.
Visible light falls in the range of the EM spectrum between infrared
(IR) and ultraviolet (UV). It has frequencies of about 4 × 1014 to 8 ×
1014 cycles per second, or hertz (Hz) and wavelengths of about
740 nanometers (nm) or 2.9 × 10−5 inches, to 380 nm (1.5 ×
10−5 inches).
Light behaves as a wave, so it to is reflected.
Therefore, an object does not need to emit photons itself to be seen, it
just has to reflect light back to our eyes where we can detect it.



Objects that do not allow light to pass through them are called
opaque.
Objects that allow light to pass through them are considered
transparent.
Objects in between are called translucent.
How do we "see" using Visible Light?
Cones in our eyes are receivers for these tiny visible light waves. The
Sun is a natural source for visible light waves and our eyes see the
reflection of this sunlight off the objects around us.
The color of an object that we see is the color of light reflected. All other
colors are absorbed.
Light bulbs are another source of visible light waves.
There are two types of color images that can be made from satellite data
- true-color and false-color. To take true-color images, like this one, the
satellite that took it used sensors to record data about the red, green,
and blue visible light waves that were reflecting off the earth's surface.
The data were combined later on a computer. The result is similar to
what our eyes see.
Here is a false-color image of Phoenix. How does it compare to the truecolor and space shuttle images on this page?
A false-color image is made when the satellite records data about
brightness of the light waves reflecting off the Earth's surface. These
brightness are represented by numerical values - and these values can
then be color-coded. It is just like painting by number.
The colors chosen to "paint" the image are arbitrary, but they can be
chosen to either make the object look realistic, or to help emphasize a
particular feature in the image.
Astronomers can even view a region of interest by using software to
change the contrast and brightness on the picture, just like the controls on
a TV. Can you see a difference in the color palettes selected for the two
images below? Both images are of the Crab Nebula, the remains of an
exploded star.
Here's another example - the below pictures show the planet Uranus in
true-color (on the left) and false-color (on the right).
The true-color has been processed to show Uranus as human eyes would
see it from the vantage point of the Voyager 2 spacecraft, and is a
composite of images taken through blue, green and orange filters. The
false color and extreme contrast enhancement in the image on the right,
brings out subtle details in the polar region of Uranus. The very slight
contrasts visible in true color are greatly exaggerated here, making it
easier to studying Uranus' cloud structure. Here, Uranus reveals a dark
polar hood surrounded by a series of progressively lighter concentric
bands. One possible explanation is that a brownish haze or smog,
concentrated over the pole, is arranged into bands by zonal motions of the
upper atmosphere.
What does Visible Light show us?
It is true that we are blind to many wavelengths of light. This makes it
important to use instruments that can detect different wavelengths of light
to help us to study the Earth and the Universe. However, since visible light
is the part of the electromagnetic spectrum that our eyes can see, our
whole world is oriented around it. And many instruments that detect visible
light can see father and more clearly than our eyes could alone. That is
why we use satellites to look at the Earth, and telescopes to look at the
Sky.
Simple Theory of Color Vision
We have already noted that color is associated with the wavelength of
visible electromagnetic radiation. When our eyes receive pure-wavelength
light, we tend to see only a few colors. Six of these (most often listed) are
red, orange, yellow, green, blue, and violet.
These are the rainbow of colors produced when white light is dispersed
according to different wavelengths. There are thousands of other hues
that we can perceive.
These include brown, teal, gold, pink, and white. One simple theory of
color vision implies that all these hues are our eye’s response to different
combinations of wavelengths. This is true to an extent, but we find that
color perception is even subtler than our eye’s response for various
wavelengths of light.
The two major types of light-sensing cells (photoreceptors) in the retina
are
rods
and
cones
Cones are most concentrated in the fovea, the central region of the retina.
There are no rods here. The fovea is at the center of the macula, a 5 mm
diameter region responsible for our central vision. The cones work best in
bright light and are responsible for high resolution vision. There are about
6 million cones in the human retina.
There are three types of cones, and each type is sensitive to different
ranges of wavelengths.
A simplified theory of color vision is that there are three primary colors
corresponding to the three types of cones. The thousands of other hues
that we can distinguish among are created by various combinations of
stimulations of the three types of cones.
Color television uses a three-color system in which the screen is covered
with equal numbers of red, green, and blue phosphor dots. The broad
range of hues a viewer sees is produced by various combinations of these
three colors.
For example, you will perceive yellow when red and green are illuminated
with the correct ratio of intensities. White may be sensed when all three
are illuminated. Then, it would seem that all hues can be produced by
adding three primary colors in various proportions. But there is an
indication that color vision is more sophisticated. There is no unique set
of three primary colors.
Another set that works is yellow, green, and blue. A further indication of
the need for a more complex theory of color vision is that various different
combinations can produce the same hue.
Yellow can be sensed with yellow light, or with a combination of red and
green, and also with white light from which violet has been removed.
The three-primary-colors aspect of color vision is well established; more
sophisticated theories expand on it rather than deny it.
Consider why various objects display color—that is, why are feathers blue
and red in a crimson rosella? The true color of an object is defined by its
absorptive or reflective characteristics.
Figure 2 shows white light falling on three different objects, one pure blue,
one pure red, and one black, as well as pure red light falling on a white
object. Other hues are created by more complex absorption
characteristics.
Pink, for example on a galah cockatoo, can be due to weak absorption of
all colors except red. An object can appear a different color under nonwhite illumination.
For example, a pure blue object illuminated with pure red light will appear
black, because it absorbs all the red light falling on it. But, the true color
of the object is blue, which is independent of illumination.
Similarly, light sources have colors that are defined by the wavelengths
they produce.
A helium-neon laser emits pure red light. In fact, the phrase “pure red light”
is defined by having a sharp constrained spectrum, a characteristic of
laser light.
The Sun produces a broad yellowish spectrum, fluorescent lights emit
bluish-white light, and incandescent lights emit reddish-white hues 3.
As you would expect, you sense these colors when viewing the light
source directly or when illuminating a white object with them.
All of this fits neatly into the simplified theory that a combination of
wavelengths produces various hues.
Perhaps the most important characteristic of visible light is color. Color is
both an inherent property of light and an artifact of the human eye. Objects
don't "have" color, according to Glenn Elert, author of the website The
Physics Hypertextbook. Rather, they give off light that "appears" to be a
color. In other words, Elert writes, color exists only in the mind of the
beholder.
Sensitivity Curve
Human eyes are not equally sensitive to all colors.
Eyes are most sensitive in the mid-range near wavelength =555 nm
Color Transmission
Filters work in a similar way.
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Red filters only let RED light thru.
Blue let only BLUE light thru.