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In this activity, you will apply the scientific method to investigate the properties of transverse waves. The activity involves experimentation using a web-based interactive simulation. The URL for the simulation is provided in the activity file.
Activity Instructions
Download the Wave on a String activityUsing a simulation, apply the scientific method to investigate the various properties of transverse waves.Background ReadingBefore attempting the activity, review the topic The Nature of Waves in Chapter 6 of The Sciences. Completing the reading is important for you to be able to correctly apply the properties of waves to the experiments performed in this activity.Introduction to the Simulation1. After completing the background reading for this assignment, go to the “Wave on a String” simulation on the PhET simulations website at http://phet.colorado.edu/en/simulation/wave-on-a-string. Click the play arrow on the simulation graphic to run the web-based simulation or click DOWNLOAD to run the simulation locally on your device.2. Get oriented to the simulation by exploring and manipulating all the possible variables and options:a. MODE: manual, oscillate, pulse. In Oscillate and Pulse modes, you can pause/play, step, and also change other settings regarding the wave characteristicsi. Amplitude: 0 to 1.25 cmii. Frequency: 0 to 3.00 Hziii. Damping: None to Lotsiv. Tension: Low to Highb. END: fixed end, loose end, or no endc. Rulers: Display (box checked) or not (box unchecked). When displayed, you will see two rulers: one horizontal and one vertical.d. Timer: display (box checked) or not (box unchecked); start/pause/resete. Reference line: dashed line that can be used as a reference for amplitude measurements Note: The rulers, timer, and reference line can all be dragged around as needed. In addition to the reference line, there is another dashed line parallel to the undisturbed string that is fixed (not moveable).f. Restart button: starts the simulation over for the current settingsg. Reset button (circular button with a circular arrow, on the lower right of the screen): resets the simulation to the default settingsh. Pause button ( I I ): simulation is running when this is showing; press to pause the simulationi. Play arrow ( > ): simulation is paused when this is showing; press to run the simulationWhile getting oriented with the simulation, think about how the different wave properties discussed in Chapter 6 are being illustrated in the simulation, and how changing things in the simulation affects the wave properties.3. After spending some time experimenting with the simulation, follow the steps below to conduct four experiments. Before beginning, be prepared to write down your observations.ExperimentsExperiment 1: Manipulating a Wave on a StringIn this experiment, you will investigate and observe the properties of waves by manipulating a string attached to an energy source.Before completing the experiment, write down a hypothesis, based on your current understanding after reading the background information for the activity, that makes specific predictions for how the string will react to changes to the energy source and to changes to the end of the string.1. Experiment setup: Click the Reset button. The Mode will be set to Manual. Set the Damping to None.2. Experiment procedure:a. Set the End to No End. Wiggle the wrench up and down at varying speeds and over various distance ranges. As the wrench is wiggled, a wave disturbance is created and the string to moving up and down represents energy being propagated along the string. Observe how the properties (wavelength, frequency, and speed) of the wave produced changes with the different wiggle action. Write down your observations.b. After wiggling for several seconds, let go of the wrench and observe what happens. Write down your observations.c. Click Restart. Change the End to Loose End. Wiggle the wrench as in part a. Observe the differences in the properties of the waves produced with the Loose End compared to No End. After wiggling for a bit, let go of the wrench and observe what happens. Write down your observations.d. Click Restart. Change the End to Fixed End. Wiggle the wrench as in part a. Observe the differences in the properties of the waves produced with the Fixed End compared to No End and the Loose End. After wiggling for a bit, let go of the wrench and observe what happens. Write down your observations.Answer the questions below to help you formulate some results and conclusions for this experiment. You may need to do some additional experimentation to answer the questions.1. In part a. of the experiment:a. Based on the definitions of transverse and longitudinal waves (chapter 6), which type of wave – transverse or longitudinal – is being generated along the string? Explain how you determined this.b. How is the wave frequency and wavelength affected when the wrench is wiggled faster?c. How is the wave amplitude affected when the wrench is wiggled farther up and down?2. For which end setting(s) is wave interference taking place? Explain what causes the interference.3. For which end setting(s) does the energy propagate away from the source without returning? Explain why the energy does not return.Experiment Results and ConclusionsBased on your observations while performing the experiment and your answers to the questions above, formulate some results and conclusions for how the string will react to changes to the energy source and changes to the end of the string.Experiment 2: The Effects of Damping and TensionIn this experiment, you will investigate and observe the effects of adding tension or damping to a wave.Before completing the experiment, write down a hypothesis, based on your understanding after reading the background information for the activity, that makes specific predictions for how adding tension in the string, or damping the energy along the wave, will affect the amplitude, wavelength, and speed of the wave being generated by the oscillator.1. Experiment setup: Click the Reset button, and then click the pause button ( I I ) so that the play arrow ( > ) is showing. Set Mode to Oscillate, set Damping to None, set Tension to Low, set end to No End, and display the Rulers. You do not need to adjust the frequency and amplitude settings. For this experiment, we will be changing the Damping and Tension settings.2. Experiment procedure:a. Click the play arrow. After the oscillation wheel has turned several times, gradually adjust the Damping from None to Lots. Observe how the amplitude, wavelength, and speed of the energy propagating along the string all change as the damping is increased, using the rulers as an aid in determining the relative changes (you do not need to take any measurements). Write down your observations.b. Repeat the setup in part 1 above.c. Click the play button. After the oscillation wheel has turned several times, gradually adjust the Tension from Low to High. Observe how the amplitude, wavelength, and speed of the energy propagating along the string change as the tension is increased, using the rulers as an aid in determining the relative changes (you do not need to take any measurements). Write down your observations.Experiment Results and Conclusions
In chapter 6, you learned that the wave period is equal to 1/frequency. So, the inverse of the corresponding frequency setting (1/frequency) and the calculated period should be very close in value.FrequencySettingTime IntervalNumber of Crests (Wave Cycles) Passing in 10 SecondsWave Period(10 seconds/number of wave cycles passing in 10 seconds)1.00 Hz 10 seconds2.00 Hz 10 secondsExperiment Results and ConclusionsExplain how the data you collected and calculations you performed in the experiment validates the relationship between wave period and wave frequency as described in Chapter 6. If your data and calculations did not validate the relationship, go back and check that you performed the experiment correctly.Activity EDS 1021
Week 4 Interactive Activity
- Wave on a String
Objective
Using a simulation, apply the scientific method to investigate the various properties of
transverse waves.
Background Reading
Before attempting the activity, review the topic The Nature of Waves in Chapter 6 of The
Sciences. Completing the reading is important for you to be able to correctly apply the
properties of waves to the experiments performed in this activity.
Introduction to the Simulation
1. After completing the background reading for this assignment, go to the “Wave on a String”
simulation on the PhET simulations website at
http://phet.colorado.edu/en/simulation/wave-on-a-string. Click the play arrow on the
simulation graphic to run the web-based simulation or click DOWNLOAD to run the
simulation locally on your device.
2. Get oriented to the simulation by exploring and manipulating all the possible variables and
options:
a. MODE: manual, oscillate, pulse. In Oscillate and Pulse modes, you can pause/play, step,
and also change other settings regarding the wave characteristics
i.
ii.
iii.
iv.
Amplitude: 0 to 1.25 cm
Frequency: 0 to 3.00 Hz
Damping: None to Lots
Tension: Low to High
b. END: fixed end, loose end, or no end
c. Rulers: Display (box checked) or not (box unchecked). When displayed, you will see two
rulers: one horizontal and one vertical.
d. Timer: display (box checked) or not (box unchecked); start/pause/reset
e. Reference line: dashed line that can be used as a reference for amplitude
measurementsNCE THROUGH THE DAY
adio
ready to go. As you begin the 90-minute
Ou tune the radio to a favorite FM music
ume to feel the beat. From time to time,
station that features traffic and weather
problems. The radio is so familiar and
what magical. How can music and news
om the radio station? How can so many
at the same time without interfering
ers, surprisingly, are intimately tied to
he electromagnetic force.
abou
6.1 The Nature of Waves
Lucenet Patrice/Phototeque Oredia/Age Fotostock America, Inc.
Waves are all around us. Waves of water travel across the surface of the ocean and crash against
the land. Waves of sound travel through the air when we listen to music. Some parts of the
United States suffer from mighty waves of rock and soil called earthquakes. All of these waves
must move through matter.
But the most remarkable waves of all can travel through an absolute vacuum at the speed of
light. The sunlight that warms you at the beach and provides virtually all of the energy neces-
sary for life on Earth is transmitted through space by just such a wave. The radio waves that
carry your favorite music, the microwaves that heat your dinner, and the X-rays your dentist
uses to check for cavities are also types of electromagnetic waves-invisible waves that carry
energy and travel at the speed of light. In this chapter, we will look at waves in general and then
focus on electromagnetic waves, which play an enormous role in our everyday life.
Waves are fascinating, at once familiar and yet somewhat odd. Waves, unlike flying can-
nonballs or speeding automobiles, have the ability to transfer energy without transferring mass.
Energy Transfer by Waves
Energy can be transferred in two forms in our everyday world: the particle and the wave.
Suppose you have a domino sitting on a table and you want to knock it over-a process that
requires transferring energy from you to the domino. One way to proceed would be to take
another domino and throw it. From the standpoint of energy, you would say that the musclesomino and
126 CHAPTER 6 WAVES AND ELECTROMAGNETIC RADIATION
RE 6-3 Waves passing a
bat reveal how wavelength,
ty, and frequency are related.
know the distance between
crests (the wavelength) and
umber of crests that pass each
d (the frequency), then you can
te the wave’s velocity.
In symbols:
wave crests going by every second (the frequency) and measure the distance
between the crests (the wavelength). From these two numbers, the speed of
the wave can be calculated.
If, for example, one wave arrives every 2 seconds and the wave crests are
6 meters apart, then the waves must be traveling 6 meters every 2 seconds-a
velocity of 3 meters per second. You might look out across the water and see a
particularly large wave crest that will arrive at the boat after four intervening
smaller waves. You would predict that the big wave is 30 meters away (five
times the wavelength) and that it will arrive in 10 seconds. That kind of infor-
mation can be very helpful if you are plotting the best course for an America’s
Cup yacht race or estimating the path of potentially destructive ocean waves.
This relationship among wavelength, velocity, and frequency can be writ-
ten in equation form:
ATIDE OF WAVES
In words: The velocity of a wave is equal to the length of each wave times the
number of waves that pass by each second.
In equation form:
wave velocity (m/s) = wavelength (m) x frequency (Hz)
EXAMPLE 6-1
v=λx f
where 2 (the Greek letter lambda) and fare common symbols for wavelength and wave fre-
quency, respectively. This simple equation holds for all kinds of waves (Figure 6-3).
127
wavelength (m)
AT THE BEACH
On a relatively calm day at the beach, ocean waves traveling 2 meters per second hit
the shore once every 5 seconds. What is the wavelength of these ocean waves?
Reasoning: We can solve for wavelength, given the wave’s velocity (2 meters per second)
and frequency (1 wave per 5 seconds, or 1/5 Hz = 0.2 Hz):
wave velocity (m/s) = wavelength (m) x frequency (Hz)
Solution: We can rearrange the equation to solve for wavelength.
=
velocity (m/s)
frequency (Hz)
(2 m/s)
0.2 Hz
= 10 m
The Two Kinds of Waves: Transverse and
Longitudinal
Imagine that a chip of bark or a piece of grass is lying on the surface of a pond when you
throw a rock into the water. When the ripples go by, the floating object and the water around
it move up and down; they do not move to a different spot. At the same time, however, the
wave crest moves in a direction parallel to the surface of the water. This means that the
motion of the wave is different from the motion of the medium on which the wave moves. This
kind of wave, where the motion is perpendicular to the direction of the wave, is called a trans-
verse wave (Figure 6-4a).Researchers, Inc.
130 CHAPTER 6 WAVES AND ELECTROMAGNETIC RADIATION
GURE 6-8 Two waves originating
om different points create
interference pattern. Bright
gions correspond to constructive
erference, while dark regions
respond to destructive
erference.
RE 6-9 Cross sections of
ering waves illustrate the
mena of (a) constructive and
tructive interference.
Constructive
interference
(a)
(b)
Destructive
interference
I
One easy way to think about what happens is to imagine
that each part of each wave carries with it a set of instructions
for the water surface-“move down 2 inches,” or “move up 1 inch.” When two waves arrive
simultaneously at a point, the surface responds to both sets of instructions. If one wave says to
move down 2 inches and the other to move up 1 inch, the result will be that the water surface
will move down a total of 1 inch. Thus each point on the surface of the water moves a different
distance up or down depending on the instructions that are brought to it by the two waves.
One possible situation is shown in Figure 6-9a. Two waves, each carrying the command “go
up 1 inch,” arrive at a point together. The two waves act together to lift the water surface to the
highest possible height it can have. By the same token, if two waves troughs, each 1-inch deep,
meet then the net change will be a trough 2 inches deep. This effect is called constructive inter-
ference, or reinforcement. On the other hand, you could have a situation like the one shown in
Figure 6-9b, where the two waves arrive at a point such that one is giving an instruction to go up
1 inch and the other to go down 1 inch. In this case, the two waves cancel each other out and the
STOP & THINK! Today’s scientists are much more con-
cerned about the ethical treatment of animals than were
naturalists of the eighteenth century. How might you con-
duct an experiment on the hearing of bats without injuring
the animals?
– Amplitude 1 inch
IC
Interference
Waves from different sources may overlap and affect each
other in the phenomenon called interference. Interference
describes what happens when waves from two different sources
come together at a single point-each wave interferes with the
other, and the observed height of the wave-the amplitude-is
simply the sum of the amplitudes of the two interfering waves.
Consider the common situation shown in Figure 6-8. Suppose
you and a friend each throw rocks into a pond at two separate
points as in the figure. The waves from each of these two points
travel outward and eventually will meet. What will happen
when the two waves come together?
Amplitude 1 inch
ELECTROMAGNETIC WAVE
Amplitude 1 inch
Amplitude 1 inch
131
Amplitude 2 inches
m
Wave amplitudes add
Wave amplitudes cancel
zero amplitudetons, which focuses
tina, where the
converted into nerve
signals are carried to
the optic nerve.
(adjusts focus)
of frequency slices or “banas exist, and many more people w
can do sa
undergo total internal reflection each time it comes to the edge of the glass. Light entering
longer ultraviolet waves can cause a chemical change in
skin pigments, a phenomenon known as tanning. This
lower-energy portion of the ultraviolet is not particularly
harmful by itself.
Shorter-wavelength (higher-energy) ultraviolet radia-
tion, on the other hand, carries more energy-enough
energy that this radiation, if absorbed by your skin cells.
can cause sunburn and other cellular damage. If the ultra-
violet wave’s energy alters your cell’s DNA. it may increase
your risk of developing skin cancer (see Chapter 23). In
fact, because ultraviolet radiation can damage living cells,
hospitals use it to sterilize equipment and kill unwanted.
bacteria.
The Sun produces intense ultraviolet radiation in both
longer and shorter wavelengths. Fortunately, our atmos-
phere absorbs much of the harmful short wavelengths and
thus shields living things. Nevertheless, if you spend much
time outdoors under a bright Sun. you should protect
exposed skin with a Sun-blocking chemical, which is trans-
parent (colorless) to visible light but reflects or absorbs
harmful ultraviolet rays before they can reach your skin
(Figure 6-26).
The energy contained in both long and short ultraviolet wavelengths can be absorbed by
atoms, which in special materials may subsequently emit a portion of that absorbed energy as
visible light. (Remember, both visible light and ultraviolet light are forms of electromagnetic
radiation, but visible light has longer wavelengths, and therefore less energy, than ultraviolet
radiation.) This phenomenon, called fluorescence, provides the so-called black light effects so
popular in stage shows and nightclubs. We’ll examine the origins of fluorescence in more detail
in Chapter 8.
X-rays
X-rays are electromagnetic waves that range in wavelength from
about 100 nanometers down to 0.1 nanometer, smaller than a
single atom. These high-frequency (and thus high-energy) waves
can penetrate several centimeters into most solid matter but are
absorbed to different degrees by all kinds of materials. This fact
allows X-rays to be used extensively in medicine to form visual
images of bones and organs inside the body. Bones and teeth
absorb X-rays much more efficiently than skin or muscle, so a
detailed picture of inner structures emerges (Figure 6-27). X-rays
are also used extensively in industry to inspect for defects in
welds and manufactured parts.
6.3 THE ELECTROMAGNETIC SPECTRUM 143
a
The X-ray machine in your doctor’s or dentist’s office is
something like a giant lightbulb with a glass vacuum tube. At
one end of the tube is a tungsten filament that is heated to a
very high temperature by an electrical current, just as in an
incandescent lightbulb. At the other end is a polished metal
plate. X-rays are produced by applying an extremely high volt-
age-negative on the filament and positive on the metal plate-
so electrons stream off the filament and smash into the metal
plate at high velocity. The sudden deceleration of the negatively
charged electrons releases a flood of high-energy electromag-
netic radiation-the X-rays that travel from the machine to you
at light speed.
Philip and Karen Smith/lconica/Getty Images
FIGURE 6-26 When you spend
time outdoors under a bright Sun,
you should protect your skin with
sunblock, which is transparent to
visible light, but reflects or absorbs
harmful ultraviolet rays.
FIGURE 6-27 Internal structures
are revealed because bones and
different tissues absorb X-rays to
different degrees.TECHNOLOGY
AM and FM Radio Transmission
Radio waves carry signals in two ways: amplitude modulation (AM) and frequency
modulation (FM). Broadcasters can send out their programs at only one narrow
range of frequencies, a situation very different from music or speech, which use
a wide range of frequencies. Thus radio stations cannot simply transform a range
of sound-wave frequencies into a similar range of radio-wave frequencies. Instead.
the information to be transmitted must be impressed in some way on the narrow
frequency range of your station’s radio waves.
This problem is similar to one you might experience if you had to send a mes
sage across a lake with a flashlight at night. You could adopt two strategies. You
could send a coded message by turning the flashlight on and off, thus varying the
brightness (the amplitude) of the light. Alternatively, you could change the color
(the frequency) of the light by alternately passing blue and red filters in front of the
beam.
6.3 THE ELECTROMAGNETIC SPECTRUM
Amplitude modulation (AM)
A. Original sound wave
B. Carrier wave
C. Modulated signal
(a)
Microwaves
Microwaves include electromagnetic waves whose wavelengths range from about 1 meter
(a few feet) to 1 millimeter (0.001 meter, or about 0.04 inch). The longer wavelengths of
microwaves travel easily through the atmosphere, like their cousins in the radio part of the
spectrum, though rock and building materials absorb most microwaves. Therefore, micro-
waves are used extensively for line-of-sight communications. Most satellites broadcast sig-
nals to Earth in microwave channels, and these waves also commonly carry long-distance
telephone calls and TV broadcasts. The satellite antennas that you see on private homes
and businesses are designed primarily to receive microwave transmissions, as are the large
cone-shaped receivers attached to the microwave relay towers found on many hills or tall
buildings.
C. Modulated signal
Radio stations also adopt these two strategies (see Figure 6-19). All stations
begin with a carrier wave of fixed frequency. AM radio stations typically broadcast
at frequencies between about 530 and 1600 kHz, whereas the carrier frequencies of
FM radio stations range from about 88 to 110 MHz.
(b)
FIGURE 6-19 (a) AM (amplitude
modulation) and (b) FM (frequency
the
The process called amplitude modulation, or AM, depends on varying the strength (or ampli-
tude) of the radio’s carrier wave according to the sound signal to be transmitted (Figure 6-19a). modulation) transmission differ in
Thus the shape of the sound wave is impressed on the radio’s carrier wave signal. When this
signal is taken into your radio, the electronics are designed so that the original sound signal is
recovered and used to run the speakers. The original sound signal is what you hear when you
turn on your radio. Because AM frequencies easily scatter off the layers of the atmosphere, they
way that a sound wave (A) is
superimposed on a carrier wave o
constant amplitude and frequency
(B). The carrier wave can be varied,
or modulated, to carry information
(C) by altering its amplitude or its
can be heard over great distances.
Alternatively, you can slightly vary the frequency of the radio’s wave according to the
signal you want to transmit, a process called frequency modulation, or FM, as shown in Figure frequency.
6-19b. A radio that receives this particular signal will unscramble the changes in frequency
and convert them into electrical signals that run the speakers so that you can hear the
original signal.
The distinctive transmission and absorption properties of microwaves make them ideal for
use in aircraft radar. Solid objects, especially those made of metal, reflect most of the micro-
waves that hit them. By sending out timed pulses of microwaves and listening for the echo, you
can judge the direction, distance (from the time it takes the wave to travel out and back), and
speed (from the Doppler effect) of a flying object. Modern military radar is so sensitive that
it can detect a single fly at a distance of a mile. To counteract this sensitivity, aircraft design-
ers have developed planes with “stealth” technology-combinations of microwave-absorbing
materials, angled shapes that reduce the apparent cross section of the plane, and electronic
Jamming to avoid detection (Figure 6-20).
139
Frequency modulation (FM)
A. Original sound wave
m
B. Carrier wave
FIGURE 6-20 The Stealth fighter
has been engineered to reflect and
absorb microwave radiation and thus
avoid detection by radar.
U.S. Air Force Photo by Staff Sgt. Andy Dunaway, Department of Defense
exhaust of jet engines in enemy aircraft, and infrared detectors are often
used to see human beings (Figure 6-22) and warm engines at night. Simi-
larly, many insects (such as mosquitoes and moths) and other nocturnal
animals (including opossums and some snakes) have developed sensitivity
to infrared radiation:; thus they can “see” in the dark.
Infrared detection i
If you
take
s also used to find heat leaks in homes and buildings.
a picture of a house on a cold night using film that is sensitive to
infrared radiation, places where heat is leaking out will show up as bright
spots on the film. This information can be used to correct the heat loss and
thus conserve energy. In a similar way, Earth scientists often monitor volca-
noes with infrared detectors. The appearance of a new “hot spot” may signal
an impending eruption.
STOP & THINK! We often say that we get heat from the Sun. What
actually travels between the Sun and Earth?
6.3 THE ELECTROMAGNETIC S
Visible Light
What we perceive as the colors of the rainbow are contained in visible light, whose wave-
lengths range from red light at about 700 nanometers down to violet light at about 400 nanom-
eters (Figure 6-23). From the point of view of the
larger universe, the visible electromagnetic world in
which we live is a very small part of the total picture
(see Figure 6-18).
FIGURE 6-22 A photograph using
infrared film reveals heat escaping
from an elephant. This “false-color”
image is coded so that white is
hottest, followed by red, pink, blue,
and black
David Parker/Photo Researchers
Our eyes distinguish several different colors, but
these portions of the electromagnetic spectrum
have no special significance except in our percep-
tions. In fact, the distinct colors that we see-red.
orange, yellow, green, blue, and violet-represent
very different-sized slices of the electromagnetic
spectrum. The red and green portions of the spec-
trum are rather broad, spanning more than 50
nanometers of frequencies; we thus perceive many
different wavelengths as red or blue. In contrast, the
yellow part of the spectrum is quite narrow, encom-
passing wavelengths from only about 570 to 590
nanometers.
Why should our eyes be so sensitive to such a
restricted range of the spectrum? The Sun’s light is especially intense in this part of the spec-
trum, so some biologists suggest that our eyes evolved to be especially sensitive to these
wavelengths, in order to take maximum advantage of the Sun’s light. Our eyes are ideally
adapted for the light produced by our Sun during daylight hours. Our eyes are also able to
see visible light produced by a wide variety of common chemical reactions (see Chapter 10).
most notably burning (Figure 6-24). By contrast, animals that hunt at night, such as owls and
cats, have eyes that are more sensitive to infrared wavelengths-radiation that makes warm
living things stand out against the cooler background.
(a)
THE SCIENCE OF LIFE
The Eye
The light detector most familiar to us is one we carry around with us all the time-the human
eye. Eyes are marvelously complex light-collecting organs that send nerve signals to the brain.
Your brain converts these signals into images through a combination of physical and chemical
processes (Figure 6-25).
100
80
Relative sensitivity
Ted Kinsman/Photo Researchers, Inc.
40
0
400 450 500 550 600 650 700
Wavelength (nm)
(b)
FIGURE 6-23 (a) A glass prism
separates light into the visible
spectrum of colors, because different
amounts. (b) Humans perceive the
wavelengths of light bend different
visible light spectrum as a sequence
of color bands. The relative sensitivity
of the human eye differs for different
wavelengths. Our perception peaks
near wavelengths that we perceive
as yellow, though the colors we see
have no special physical significance.
