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KEY CONCEPT
Waves have measurable
properties.
BEFORE, you learned
NOW, you will learn
• Forces cause waves
• Waves transfer energy
• Waves can be transverse
or longitudinal
• How amplitude, wavelength,
and frequency are measured
• How to find a wave’s speed
VOCABULARY
THINK ABOUT
crest p. 497
trough p. 497
amplitude p. 497
wavelength p. 497
frequency p. 497
How can a wave
be measured?
This enormous wave moves the
water high above sea level as it
comes crashing through. How
could you find out how high a
water wave actually goes? How
could you find out how fast it
is traveling? In what other ways
do you think a wave can be
measured? Read on to find out.
Waves have amplitude, wavelength,
and frequency.
COMBINATION NOTES
Use combination notes
in your notebook to
describe how waves can
be measured.
The tallest ocean wave ever recorded was measured from the deck of a
ship during a storm. An officer on the ship saw a wave reach a height
that was level with a point high on the ship, more than 30 meters
(100 ft)! Height is a property of all waves—from ripples in a glass of
water to gigantic waves at surfing beaches—and it can be measured.
The speed of a water wave is another property that can be
measured—by finding the time it takes for one wave peak to travel
a set distance. Other properties of a wave that can be measured
include the time between waves and the length of a single wave.
Scientists use the terms amplitude, wavelength, and frequency to
refer to some commonly measured properties of waves.
check your reading
496 Unit 4: Waves, Sound, and Light
What are three properties of a wave that can be measured?
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Measuring Wave Properties
A crest is the highest point, or peak, of a wave. A trough is
the lowest point, or valley, of a wave. Suppose you are riding
on a boat in rough water. When the boat points upward and
rises, it is climbing to the crest of a wave. When it points
downward and sinks, the boat is falling to the trough of
the wave.
1
crest
trough
for a transverse wave is the distance between a
line through the middle of a wave and a crest or trough. In
an ocean wave, amplitude measures how far the wave rises above, or
dips below, its original position, or rest position.
Amplitude
Amplitude is an important measurement, because it indicates
how much energy a wave is carrying. The bigger the amplitude, the
more energy the wave has. Find amplitude on the diagram below.
2
The distance from one wave crest to the very next crest is called
the wavelength. Wavelength can also be measured from trough
to trough. Find wavelength on the diagram below.
3
The number of waves passing a fixed point in a certain amount of
time is called the frequency. The word frequent means “often,” so
frequency measures how often a wave occurs. Frequency is often
measured by counting the number of crests or troughs that pass by
a given point in one second. Find frequency on the diagram below.
check your reading
VOCABULARY
Remember to add a four
square to your notebook
for each new term on
this page.
How is amplitude related to energy?
Distance above or below rest position
Wave Properties
crest
2
Wavelength is the distance from
one crest or trough to the next.
water level
at rest
fixed point
1
Amplitude is
the distance a
medium moves
above or below its
position at rest.
3
trough
Frequency is the number
of waves passing a fixed
point in a certain amount
of time.
How many wavelengths are shown in this diagram? How do you know?
Chapter 15: Waves 497
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low frequency,
long wavelength
high frequency,
short wavelength
reminder
Frequency is the number of
waves that pass a given
point in a certain amount
of time.
How Frequency and Wavelength Are Related
The frequency and wavelength of a wave are related. When frequency
increases more wave crests pass a fixed point each second. That means
the wavelength shortens. So, as frequency increases, wavelength
decreases. The opposite is also true—as frequency decreases,
wavelength increases.
Suppose you are making waves in a rope. If you make one wave crest
every second, the frequency is one wave per second (1/s). Now suppose
you want to increase the frequency to more than one wave per second.
You flick the rope up and down faster. The wave crests are now closer
together. In other words, their wavelengths have decreased.
Graphing Wave Properties
The graph of a transverse wave looks much like a wave itself. The
illustration on page 499 shows the graph of an ocean wave. The measurements for the graph come from a float, or buoy (BOO-ee), that
keeps track of how high or low the water goes. The graph shows the
position of the buoy at three different points in time. These points are
numbered. Since the graph shows what happens over time, you can
see the frequency of the waves.
Unlike transverse waves, longitudinal waves look different from
their graphs. The graph of a longitudinal wave in a spring is drawn
below. The coils of the spring get closer and then farther apart as the
wave moves through them.
wavelength
Distance
between coils
wavelength
VISUALIZATION
CLASSZONE.COM
Watch the graph of a
wave form.
amplitude
The shape of the graph resembles the shape of a transverse wave.
The wavelength on a longitudinal wave is the distance from one
compression to the next. The amplitude of a longitudinal wave
measures how compressed the medium gets. Just as in a transverse
wave, frequency in a longitudinal wave is the number of waves passing
a fixed point in a certain amount of time.
check your reading
498 Unit 4: Waves, Sound, and Light
How are longitudinal waves measured?
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Graphing a Wave
The graph of a transverse wave looks
like a wave itself. The graph shows
what happens over time.
The buoy moves up and
down as the waves pass.
2
Time: 0 s The buoy is
below the rest position.
Time: 1 s The buoy is
equal with the rest position.
3
Time: 2 s The buoy is
above the rest position.
water level
at rest
wavelength
Distance above or below rest position (m)
1
0.2
3
0.1
0
2
amplitude = 0.2 m
–0.1
frequency = 0.25/s
–0.2
1
0
1
2
3
4
Time (s)
How many seconds does it take for one wave to pass?
How much of the wave passes in one second?
Chapter 15: Waves 499
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Frequency
How can you change frequency?
PROCEDURE
1
Tie 3 washers to a string. Tape the string to the side of your desk so
that it can swing freely. The swinging washers can model wave action.
2 Pull the washers slightly to the side and let go. Find the frequency by
counting the number of complete swings that occur in 1 minute.
3 Make a table in your notebook to record both the length of the
SKILL FOCUS
Collecting data
MATERIALS
•
•
•
•
•
3 metal washers
piece of string
tape
stopwatch
meter stick
TIME
30 minutes
string and the frequency.
4 Shorten the string by moving and retaping it. Repeat for 5 different lengths.
Keep the distance you pull the washers the same each time.
WHAT DO YOU THINK?
• How did changing the length of the string affect the frequency?
• How does this model represent a wave? How does it differ from a wave?
CHALLENGE How could you vary the amplitude of this model?
Predict how changing the amplitude would affect the frequency.
Wave speed can be measured.
In addition to amplitude, wavelength, and frequency, a wave’s speed
can be measured. One way to find the speed of a wave is to time how
long it takes for a wave to get from one point to another. Another way
to find the speed of a wave is to calculate it. The speed of any wave can
be determined when both the frequency and the wavelength are
known, using the following formula:
reminder
Speed = wavelength • frequency
S = f
The symbol represents
wavelength.
Different types of waves travel at very different speeds. For example,
light waves travel through air almost a million times faster than sound
waves travel through air. You have experienced the difference in wave
speeds if you have ever seen lightning and heard the thunder that comes
with it in a thunderstorm. When lightning strikes far away, you see the
light seconds before you hear the clap of its thunder. The light waves
reach you while the sound waves are still on their way.
How fast do you think water waves can travel? Water waves travel
at different speeds. You can calculate the speed using wavelength and
frequency.
500 Unit 4: Waves, Sound, and Light
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Suppose you wish to calculate the speed of an ocean wave with
a wavelength of 16 meters and a frequency of 0.31 wave per second.
When working through the problem in the example below, it is
helpful to think of the frequency as
RESOURCE CENTER
CLASSZONE.COM
ƒ = 0.31 (wave)/s
even though the units for frequency are just 1/second. You can think
of wavelengths as “meters per wave,” or
Find out more about
wave speed.
= 16 m/(wave)
Calculating Wave Speed
Sample Problem
An ocean wave has a wavelength of 16 meters and a frequency of
0.31 wave per second. What is the speed of the wave?
What do you know? wavelength = 16 m,
(wave)
s
frequency = 0.31 What do you want to find out? Speed
Write the formula: S = f
m
(wave)
• 0.31 (wave)
s
Substitute into the formula: S = 16 m
(wave)
m
=5 • 0.31 (wave)
s
s
Calculate and simplify: 16 Check that your units agree: Unit is m/s. Unit for speed is m/s.
Units agree.
`
Answer: S = 5 m/s
Practice the Math
1. In a stormy sea, 2 waves pass a fixed point every second, and the waves are
10 m apart. What is the speed of the waves?
2. In a ripple tank, the wavelength is 0.1 cm, and 10 waves occur each second.
What is the speed of the waves (in cm/s)?
KEY CONCEPTS
CRITICAL THINKING
1. Make a simple diagram of a
wave, labeling amplitude,
frequency, and wavelength.
For frequency, you will need
to indicate a span of time,
such as one second.
3. Observe Suppose you are
watching water waves pass
under the end of a pier. How
can you figure out their
frequency?
2. What two measurements of a
wave do you need to calculate
its speed?
4. Calculate A wave has a
speed of 3 m/s and a frequency
of 6 (waves)/s. What is its
wavelength?
CHALLENGE
5. Apply Imagine you are on a
boat in the middle of the sea.
You are in charge of recording
the properties of passing ocean
waves into the ship’s logbook.
What types of information
could you record? How would
this information be useful?
Explain your answer.
Chapter 15: Waves 501