CS_Ch3_LetUsEntertain 6/8/06 1:56 PM Page 144

Let Us Entertain You

Activity 1 Making Waves

GOALS What Do You Think?

In this activity you will:
On December 26, 2004, one of the largest
• Observe the motion of a pulse.
tsunamis (tidal waves) hit many countries
• Measure the speed of a wave.
in the Indian Ocean in Southeast Asia,
• Observe standing waves. causing massive damage. Some of the waves reached
• Investigate the relationship almost 35 meters (100 feet) in height.
among wave speed,
wavelength, and frequency.
• How does water move to make a wave?
• Make a model of wave motion.
• How does a wave travel?

Record your ideas about these questions in your Active

Physics log. Be prepared to discuss your responses with
your small group and with your class.

144
Active Physics
CS_Ch3_LetUsEntertain 2/24/05 11:04 PM Page 145

Activity 1 Making Waves

For You To Do
1. In an area free of obstacles, stretch out a Slinky® so the
turns are a few centimeters apart. Mark the positions of the
end of the Slinky by sticking pieces of tape on the floor.
Measure the distance between the pieces of tape.
a) Record the distance between the pieces of tape in your log.

2. With the Slinky stretched out to the tape, grab the spring
near one end, as shown in the drawing, and pull sideways
20 cm and back. To move it correctly, move your wrist as if
snapping a whip. Observe what happens. You have made a
transverse pulse.
a) In what direction does the spring move as the pulse goes by?
b) A dictionary definition of transverse is: “Situated or lying
across.” Why is transverse a good name for the wave you
observed?

Amplitude = 20 cm

c) Measure and record the amplitude of the wave. The

distance you disturbed the spring is called the amplitude.
The amplitude tells how much the spring is displaced.

3. After you have experimented with making pulses, measure

the speed of the pulse. You will need to measure the time it
takes the pulse to go the length of the spring. Take several
measurements and then average the values.
a) Record your data in the second and third rows of a table
like the one on the following page.

145
Coordinated Science for the 21st Century
CS_Ch3_LetUsEntertain 2/24/05 11:04 PM Page 146

Let Us Entertain You

Time for pulse to

length of spring
Amplitude travel from one Average time Speed = average time
end to the other

4. Measure the speed of the pulses for two other amplitudes,

one larger and one smaller than the value used in Step 3.
a) Record the results in the table in your log.
b) How does the speed of the pulse depend on the amplitude?

5. Now make waves! Swing one end back and forth over and over
again along the floor. The result is called a periodic wave.
a) Describe the appearance of the periodic wave you created.

6. To make these waves look very simple, change the way you
swing the end until you see large waves that do not move along
the spring. You will also see points where the spring does not
move at all. These waves are called standing waves.

7. The distance from one crest (peak)

Crest
of a wave to the next is called the
wavelength. Notice that you can find
Amplitude the wavelength by looking at the points
where the spring does not move. The
wavelength is twice the distance
between these points. Measure the
1 wavelength wavelength of your standing wave.
Trough
Standing wave a) Record the wavelength of your
standing wave in your log.

8. You can also measure the wave frequency. The frequency is the
number of times the wave moves up and down each second.
Measure the frequency of your standing wave. (Hint: Watch
the hands of the person shaking the spring. Time a certain
number of back-and-forth motions. The frequency is the
number of back-and-forth motions of the hand in one second.)

146
Active Physics
CS_Ch3_LetUsEntertain 3/3/05 11:08 AM Page 147

Activity 1 Making Waves

a) Record the wave frequency in your log. The unit of

frequency is the hertz (Hz).

9. Make several different standing waves by changing the wave

frequency. Try to make each standing wave shown in the
drawings (at right). Measure the wavelength. Measure the
frequency.
a) Record both in a table like the one below.

Wavelength Frequency Speed (m/s)

(m/cycle) (cycles/s or Hz) wavelength  frequency

Wavelength = twice Slinky length

Wavelength = Slinky length

b) For each wave, calculate the product of the wavelength

and the frequency. Compare these values with the average
speed of the pulse that you found in Steps 3 and 4 above.

10. All the waves you have made so far are transverse waves.
A different kind of wave is the compressional (or Wavelength = 2/3 Slinky length

longitudinal) wave. Have the members of your group stretch

out the Slinky between the pieces of tape and hold the ends
firmly. To make a compressional wave, squeeze part of the
spring and let it go. Measure the speed of the compressional
wave and compare it with the speed of the transverse wave.
Wavelength

a) Record your results in a table partly like the one after

Step 3.
b) In what direction does the Slinky move as the wave goes by?

147
Coordinated Science for the 21st Century
CS_Ch3_LetUsEntertain 2/24/05 11:04 PM Page 148

Let Us Entertain You

c) A dictionary definition of compressional is: “a. The act or

process of compressing. b. The state of being compressed.”
A dictionary definition of longitudinal is: “Placed or
Physics Words
running lengthwise.” Explain why compressional or
periodic wave: a
repetitive series of pulses; longitudinal wave is a suitable name for this type of wave.
a wave train in which the
particles of the medium 11. To help you understand waves better, construct a wave viewer
undergo periodic motion by cutting a slit in a file card and labeling it as shown.
(after a set amount of
time the medium returns
to its starting point and
2.0 cm
begins to repeat its
motion). 1.5 cm
crest: the highest point of 1.0 cm
displacement of a wave. 0.5 cm
trough: the lowest point 0.0 cm
on a wave.
–0.5 cm
amplitude: the maximum
displacement of a particle –1.0 cm
as a wave passes; the –1.5 cm
height of a wave crest; it
is related to a wave’s –2.0 cm
energy.

12. Make a drawing of a transverse wave on a strip of adding

machine tape. Place this strip under the wave viewer so you
can see one part of the wave through the slit.

13. With the slit over the tape, pull the tape so that the wave
moves. You will see a part of the wave (through the slit)
going up and down.

14. Draw waves with different wavelengths on other pieces of

adding machine tape. Put these under the slit and pull the
adding machine tape at the same speed.
a) Describe what you see.

148
Active Physics
CS_Ch3_LetUsEntertain 2/24/05 11:04 PM Page 149

Activity 1 Making Waves

FOR YOU TO READ red part of the Slinky would not move across
the room.The Slinky wave moves, but the parts
Wave Vocabulary
of the Slinky remain in the same place as the
In this activity, you were able to send wave passes by. A wave can be defined as a
energy from one end of the Slinky to the transfer of energy with no net transfer of mass.
other.You used chemical energy in your
muscles to create mechanical energy in your Leonardo da Vinci stated that “the wave flees
arms that you then imparted to the Slinky.The the place of creation, while the water does
Slinky had energy. A card at the other end of not.” The water moves up and down, but the
the Slinky would have moved once the wave wave moves out from its center.
arrived there.The ability to move the card is an
In discussing waves, a common vocabulary
indication that energy is present.The total
helps to communicate effectively.You observed
energy is transferred but it is always
waves in the lab activity.We will summarize
conserved.
some of the observations here and you can
Of course, you could have used that same become more familiar with the terminology.
mechanical energy in your arm to throw a ball
across the room.That would also have 6.00
transferred the energy from one side of the crest
room to the other. It would have also moved 4.00

amplitude
the card.
2.00

0.00
1 2 3 4 5 6 7
–2.00

–4.00 one
wavelength
trough 1λ
–6.00

A periodic wave is a repetitive series of

pulses. In the periodic wave shown in the
diagram above, the highest point is called the
There is a difference between the Slinky crest. The lowest point is called the trough.
transferring the energy as a wave and the ball The maximum disturbance, the amplitude, is
transferring the energy.The Slinky wave 5.00 cm. Notice that this is the height of the
transferred the energy, but the Slinky basically crest or the height of the trough. It is not the
stayed in the same place. If the part of the distance from the crest to the trough.
Slinky close to one end were painted red, the
➔

149
Coordinated Science for the 21st Century
CS_Ch3_LetUsEntertain 2/24/05 11:04 PM Page 150

Let Us Entertain You

The wavelength of a periodic wave is the per second.The period would be the time for
distance between two consecutive points in one wave to pass the point, which equals
1
phase.The distance between two crests is one  second. Mathematically, this relationship
10
wavelength or 1 . (The Greek letter lambda is can be represented as:
used to signify wavelength.) The wavelength of 1 1
the wave in the diagram is 2.5 cm. T =  or f = 
f T
The amplitude of a periodic wave is the Points in a periodic wave can be “in phase”
maximum disturbance. A large amplitude if they have the same displacement and are
corresponds to a large energy. In sound, the moving in the same direction. All crests of the
large amplitude is a loud sound. In light, the wave shown below are “in phase.”
large amplitude is a bright light. In Slinkies, the
large amplitude is a large disturbance. 6.00
A B
The wavelength of the wave in the diagram is 4.00
2.5 cm. It is the distance between two crests
or the distance between two troughs. 2.00 C D

E F
The frequency is the number of vibrations 0.00
1 2 3 4 5 6 7
occurring per unit time. A frequency of
10 waves per second may also be referred –2.00
to as 10 vibrations per second, 10 cycles per
–4.00
second, 10 per second, 10 s1, 10 Hz (hertz).
The human ear can hear very low sounds
–6.00
(20 Hz) or very high sounds (20,000 Hz).You
can’t tell the frequency by examining the wave In the wave shown, the following pairs of
in the diagram.The “snapshot” of the wave is at points are in phase A and B, C and D, E and F.
an instant of time.To find the frequency, you
have to know how many crests pass by a point A node is a spot on a standing wave where
in a given time. the medium is motionless.There are places
along the medium that do not move as the
The period, T, of a wave is the time it takes to standing wave moves up and down.The
complete one cycle. It is the time required for locations of these nodes do not change as the
one crest to pass a given point.The period and standing wave vibrates. A transverse wave is
the frequency are related to one another. If a wave in which the motion of the medium is
three waves pass a point every second, the perpendicular to the motion of the wave. A
frequency is three waves per second.The longitudinal wave is a wave in which the
period would be the time for one wave to pass motion of the medium is parallel to the
the point, which equals 1 s. If 10 waves pass a direction of the motion of the wave.
3
point every second, the frequency is 10 waves

150
Active Physics
CS_Ch3_LetUsEntertain 2/24/05 11:05 PM Page 151

Activity 1 Making Waves

PHYSICS TALK
Calculating the Speed of Waves
You can find the speed of a wave by measuring the
distance the crest moves during a certain change in time.
change in distance
speed =
change in time Physics Words
wavelength: the distance
In mathematical language: between two identical
points in consecutive
∆d cycles of a wave.
v=
∆t frequency: the number of
waves produced per unit
where v = speed time; the frequency is the
reciprocal of the amount
d = distance of time it takes for a
single wavelength to pass
t = time a point.
Suppose the distance the crest moves is 2 m in 0.2 s. The period: the time required
to complete one cycle of
speed can be calculated as follows: a wave.

v= ∆d node: a point on a
standing wave where the
∆t medium is motionless.
= 2m transverse pulse or wave:
a pulse or wave in which
0.2 s the motion of the
= 10 m/s medium is perpendicular
to the motion of the
wave.
The distance from one crest of a wave to the next is the
longitudinal pulse or
wavelength. The number of crests that go by in one second wave: a pulse or wave in
is the frequency. Imagine you saw five crests go by in one which the motion of the
second. You measure the wavelength to be 2 m. The medium is parallel to the
direction of the motion
frequency is 5 crests/second, so the speed is (5  2) = 10 m/s. of the wave.
Thus, the speed can also be found by multiplying the
wavelength and the frequency.
speed = frequency  wavelength
In mathematical language:
v = ƒ
where v = speed
ƒ = frequency
 = wavelength ➔

151
Coordinated Science for the 21st Century
CS_Ch3_LetUsEntertain 2/24/05 11:05 PM Page 152

Let Us Entertain You

Standing waves happen L

anywhere that the length of the
Slinky and the wavelength have a
particular mathematical
relationship. The length of the
1
Slinky must equal 2 wavelength,
1
1 wavelength, 1 2 wavelengths,
2 wavelengths, etc.
Mathematically, this can be
stated as:
n
L = 
2
where L is the length
of the Slinky,
 is the wavelength
n is a number (1, 2, 3…)

Sample Problem 1
You and your partner sit on the floor and stretch out a
Slinky to a length of 3.5 m. You shake the Slinky so that it
forms one loop between the two of you. Your partner times
10 vibrations and finds that it takes 24.0 s for the Slinky
to make these vibrations.

a) How much of a wave have you generated and what is

the wavelength of this wave?

Strategy: Draw a sketch of the wave you have made and

you will notice that it looks like one-half of a total wave. It
is! This is the maximum wavelength that you can produce
on this length of Slinky. You can use the equation that
shows the relationship between the length of the Slinky
and the wavelength.

Givens:

L = 3.5 m
n=1

152
Active Physics
CS_Ch3_LetUsEntertain 2/24/05 11:05 PM Page 153

Activity 1 Making Waves

Solution:
n
L = 
2
Rearrange the equation to solve for .
2L
 = 
n
2 (3.5 m)
= 
1
= 7.0 m

b) What is the period of vibration of the wave?

Strategy: The period is the amount of time for one

vibration. You have the amount of time for 10 vibrations.

Solution:
time for 10 vibrations 24.0 s
T =  =  = 2.4 s
10 10

c) Calculate the wave frequency.

Strategy: The frequency represents the number of

vibrations per second. It is the reciprocal of the period.

Given:

T = 2.4 s

Solution:

number of vibrations 1
f =  or f = 
time T
1
= 
2.4 s
= 0.42 vibrations per second
= 0.42 s1 or 0.42 Hz

153
Coordinated Science for the 21st Century
CS_Ch3_LetUsEntertain 2/24/05 11:34 PM Page 154

Let Us Entertain You

d) Determine the speed of the wave you have generated

on the Slinky.

Strategy: The speed of the wave may be found by

multiplying the frequency times the wavelength.

Givens:
f = 0.42 Hz
 = 7.0 m

Solution:
v = f
= 0.42 Hz  7.0 m
= 29 m/s

Remember that Hz may also be written as 1/s so the unit

of speed is m/s.

Sample Problem 2
You stretch out a Slinky to a length of 4.0 m, and your
partner generates a pulse that takes 1.2 s to go from one
end of the Slinky to the other. What is the speed of the
wave on the Slinky?

Strategy: Use your kinematics equation to determine the

speed.

Givens:
d = 4.0 m
t = 1.2 s

Solution:
d
v = 
t
4.0 m
= 
1.2 s
= 3.3 m/s

154
Active Physics
CS_Ch3_LetUsEntertain 2/24/05 11:34 PM Page 155

Activity 1 Making Waves

Reflecting on the Activity and the Challenge

Slinky waves are easy to observe. You have created transverse
and compressional Slinky waves and have measured their
speed, wavelength, and frequency. For the Chapter
Challenge, you may want to create musical instruments. You
will receive more guidance in doing this in the next activities.
Your instruments will probably not be made of Slinkies. You
may, however, use strings that behave just like Slinkies. When
you have to explain how your instrument works, you can relate
its production of sound in terms of the Slinky waves that you
observed in this activity.

Physics To Go
1. a) Four characteristics of waves are amplitude, wavelength,
frequency, and speed. For each characteristic, tell how you
measured it when you worked with the Slinky.
b) For each characteristic, give the units you used in your
measurement.
c) Which wave characteristics are related to each other?
Tell how they are related.

2. a) Suppose you shake a long Slinky slowly back and forth.

Then you shake it rapidly. Describe how the waves change
when you shake the Slinky more rapidly.
b) What wave properties change?
c) What wave properties do not change?

3. Suppose you took a photograph of a wave on a Slinky. How

can you measure wavelength by looking at the photograph?

4. Suppose you mount a video camera on a tripod and aim the

camera at one point on a Slinky. You also place a clock next
to the Slinky, so the video camera records the time. When
you look at the video of a wave going by on the Slinky, how
could you measure the frequency?

5. a) What are the units of wavelength?

b) What are the units of frequency?
c) What are the units of speed?
d) Tell how you find the wave speed from the frequency and
the wavelength.

155
Coordinated Science for the 21st Century
CS_Ch3_LetUsEntertain 2/24/05 11:34 PM Page 156

Let Us Entertain You

e) Using your answer to Part (d), show how the units of

speed are related to the units of wavelength and
frequency.

6. a) What is a standing wave?

b) Draw a standing wave.
c) Add labels to your drawing to show how the Slinky moves.
d) Tell how to find the wavelength by observing a standing
wave.

7. a) Explain the difference between transverse waves and

compressional waves.
b) Slinky waves can be either transverse or compressional.
Describe how the Slinky moves in each case.

8. a) When you made standing waves, how did you shake the
spring (change the frequency) to make the wavelength
shorter?
b) When you made standing waves, how did you shake the
spring (change the frequency) to make the wavelength
longer?

9. Use the wave viewer and adding machine tape to

investigate what happens if the speed of the wave
increases. Pull the tape at different speeds and report
your results.

10. A Slinky is stretched out to 5.0 m in length between you

and your partner. By shaking the Slinky at different
frequencies, you are able to produce waves with one loop,
two loops, three loops, four loops, and even five loops.
a) What are the wavelengths of each of the wave patterns
you have produced?
b) How will the frequencies of the wave patterns be related
to each other?

11. A tightrope walker stands in the middle of a high wire that

is stretched 10 m between the two platforms at the ends of
the wire. He is bouncing up and down, creating a standing
wave with a single loop and a period of 2.0 s.

156
Active Physics
CS_Ch3_LetUsEntertain 2/24/05 11:34 PM Page 157

Activity 1 Making Waves

a) What is the wavelength of the wave he is producing?

b) What is the frequency of this wave?
c) What is the speed of the wave?

12. A clothesline is stretched 9 m between two trees. Clothes

are hung on the line as shown in the diagram. When a
particular standing wave is created in the line, the clothes
remain stationary.

9m
3m 3m 3m

a) What is the term for the positions occupied by

the clothes?
b) What is the wavelength of this standing wave?
c) What additional wavelengths could exist in the line such
that the clothes remain stationary?

13. During the Slinky lab, your partner generates a wave pulse
that takes 2.64 s to go back and forth along the Slinky.
The Slinky stretches 4.5 m along the floor. What is the
speed of the wave pulse on the Slinky?

14. A drum corps can be heard practicing at a distance of

1.6 km from the field. What is the time delay between
the sound the drummer hears (d = 0 m) and the sound
heard by an individual 1.6 km away? (Assume the
speed of sound in air to be 340.0 m/s.)

157