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Student Exploration: Waves

Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.

Vocabulary: amplitude, compression, crest, frequency, linear mass density, longitudinal wave, medium, period,
power, rarefaction, transverse wave, trough, wave, wavelength, wave speed

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

1. A buoy is anchored to the ocean floor. A large wave approaches the buoy. How
will the buoy move as the wave goes by?

The buoy moves up and down because it follows the waves.

2. The two images show side views of ocean waves. How are the two sets of waves different?

The first waves have a higher frequency and a

higher crest than the other waves.

Gizmo Warm-up
Ocean swells are an example of waves. In the Waves Gizmo, you will observe
wave motion on a model of a spring. The hand can move the spring up and
down or back and forth.

To begin, check that the Type of wave is Transverse, Amplitude is 20.0 cm, Frequency is 0.75 Hz, Tension
is 3.0 N, and Density is 1.0 kg/m. (Note: In this Gizmo, “density” refers to the linear mass density, or mass
per unit length. It is measured in units of kilograms per meter.)

1. Click Play ( ). How would you describe the motion of a transverse wave? Click Pause ( ). Notice the
crests (high points) and troughs (low points) of the wave.

The crests and the troughs change positions with each other.

2. Click Reset ( ). Choose the Longitudinal wave and increase the Amplitude to 20.0 cm. Click Play.
How would you describe the motion of a longitudinal wave? Click Pause. Notice the compressions in the
wave where the coils of the spring model are close together and the rarefactions where the coils are
spread apart.

The longitudinal waves push forward and make highly compressed areas while other areas
are not so compressed.

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 Get the Gizmo ready:
Activity A:
● Click Reset. Select Transverse waves.
Measuring waves ● Set Amplitude to 20.0 cm, Frequency to 1.0 Hz,
Tension to 2.0 N, and Density to 2.0 kg/m.

Question: How do we measure and describe waves?

1. Observe: Click Play. Observe the motions of the hand and of the green dot in the middle.

A. What is the motion of the hand? The hand goes up and down.

B. Turn off the Lights on the checkbox and The green dot goes up and down.
observe the green dot. What is the motion of
the green dot?

C. Follow the motion of a single crest of the The crest moves from the left side all
wave. How does the crest move? the way to the right.
In a transverse wave, the motion of the medium (what the wave moves through—in this case, the spring)
is perpendicular to the direction of the wave. So, each point of the spring moves up and down as the wave
travels from left to right.

2. Measure: With the lights on, click Pause. Turn on Show rulers.

A. Use the horizontal ruler to measure the horizontal distance The wave length is
between two crests. What is this distance? 100 cm.
This is the wavelength of the wave.
B. What is the distance between the two troughs? This is also 100.

The wavelength can be found by measuring the distance between two successive crests, two
successive troughs, or any two equivalent points on the wave.

C. Click Reset. Set the Density to 1.0 kg/m. Click Play, and then This is 140 cm.
Pause. What is the wavelength of this wave?
3. Measure: Click Reset. The amplitude of a transverse wave is the maximum distance a point on the wave
is displaced, or moved, from its resting position. Turn off the lights. Click Play, and then click Pause. Use
the vertical ruler to measure the height of the green trace, showing how far the green dot moved up and
down.
A. What is the height of the green trace? The height
of the green
trace is
about 40 cm.

B. The wave’s amplitude is equal to half of this height. What is the The
amplitude? amplitude is
20 cm.

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4. Observe: Click Reset. Select Lights on and turn off Show rulers. Select Longitudinal waves. Check that
the Amplitude is 10.0 cm, the Frequency is 1.00 Hz, and the Tension is 2.0 N. Set the Density to 1.0
kg/m, and click Play.
A. What is the motion of the hand? The hand moves forward and backward.

B. Turn the lights off. What is the motion of the It moves forward and backward just like
green dot? the hand.

C. Follow the motion of a single compression of This compression moves from the left to
the wave. How does the compression the right.
move?
In a longitudinal wave, the motion of the medium is parallel to the direction of the wave. So, each
point of the spring moves back and forth as the wave is transmitted from left to right.

5. Measure: With the lights on, click Pause. Turn on Show rulers.
A. The wavelength of a longitudinal wave is equal to the distance between The
two successive compressions (or rarefactions). What is this distance? distance
is about
140 cm.

B. How does this compare to the wavelength of the comparable transverse They are
wave? (See your answer to question 2C.) about the
same
length.
6. Measure: Click Reset. The amplitude of a longitudinal wave is equal to the distance a point on the wave is
displaced from its resting position. Turn off the lights. Click Play, and then click Pause. Use the horizontal
ruler to measure the width of the green trace.
A. What is the width of the green trace? The width of
the green
trace is
about 20 cm.

B. The wave’s amplitude is equal to half of this height. What is the The
amplitude? amplitude is
10 cm.
7. Calculate: Click Reset. Select Transverse waves. Select Lights on and Show grid and turn off Show
rulers. Set the Frequency to 0.50 Hz. A single cycle is the time it takes the hand to move up, move down,
and then back up to the starting position. Click Play, and then click Pause after exactly one cycle. (This
may take a few tries.)
A. How long does one cycle take? 2 seconds
This is the period (T) of the wave.

½ hz
B. Frequency (f) is equal to 1 divided by the period: f = .
Frequency is measured in hertz (Hz), where 1 Hz = 1
cycle/sec.
What is the frequency of this wave?

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 Get the Gizmo ready:
Activity B:
● Click Reset. Check that Transverse is selected.
Wave dynamics ● Set Amplitude to 20.0 cm, Frequency to 0.75 Hz,
Tension to 3.0 N, and Density to 1.0 kg/m.

Question: What factors affect the wavelength, speed, and power of waves?

1. Record: The speed of a wave is the distance a wave pulse travels per second. The wave speed is
displayed below the spring. Click Play. What is the wave speed?

173.2 cm/s

2. Experiment: The wavelength and speed of a wave can be influenced by many factors. Adjust the
amplitude, frequency, tension, and density as described in the table below. Then report whether this causes
the wavelength and wave speed to increase or decrease. Return each variable to its original value after
each experiment.

Adjustment Effect on wavelength Effect on wave speed

Increase amplitude Increased Same
Increase frequency Decreased Same
Increase tension Increased Increased
Increase density Decreased Decreased

3. Analyze: Click Reset. Set the Frequency to 0.80 Hz, Tension to 2.0 N, and Density to 2.0 kg/m. Click
Play, and then click Pause. Turn on Show rulers.

A. What is the wavelength? 125 cm

B. What is the wave speed? 100 cm/s

C. How are the wavelength, frequency, and They are all measured from trough to
wave speed related? In general, the wave trough.
speed (v) can be calculated from the
frequency (f) and wavelength (λ) using the
formula v = f • λ.

D. What is the wavelength of a wave with f = 172.11 cm

0.9 Hz and v = 154.9 cm/s? To check, set
Frequency to 0.90 Hz, Tension to 2.4 N,
and Density to 1.0 kg/m.

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 E. Change the Density to 1.5 kg/m, and click 114.74 cm
Play. Based on the wave speed, what do
you expect the wavelength to be? Measure
the wavelength to check.

4. Gather data: Click Reset, and turn off Show rulers. The power of a wave is the amount of energy it
transmits each second. The power of the wave is displayed below the spring when Play is pressed. Record
the wave power for each of the settings below.

Amplitude Frequency Tension Density Power

20.0 cm 0.60 Hz 2.0 N 1.0 kg/m 0.402 W
40.0 cm 0.60 Hz 2.0 N 1.0 kg/m 1.61 W

20.0 cm 0.50 Hz 2.0 N 1.0 kg/m 0.279 W

20.0 cm 1.00 Hz 2.0 N 1.0 kg/m 1.12 W

20.0 cm 0.60 Hz 2.0 N 1.0 kg/m 0.402 W

20.0 cm 0.60 Hz 4.0 N 1.0 kg/m 0.568 W

20.0 cm 0.60 Hz 2.0 N 0.5 kg/m 0.284 W

20.0 cm 0.60 Hz 2.0 N 1.0 kg/m 0.402 W

Which factors increased the power of the wave?

Density, tension, amplitude, frequency.

5. Compare: Click Reset. Select Longitudinal waves. Set Amplitude to 20.0 cm, Frequency to 0.60 Hz,
Tension to 2.0 N, and Density to 1.0 kg/m. Click Play.

A. What is the power of this longitudinal wave? 0.402 W

B. Compare this power to the power of a transverse wave with the same settings. Does changing the
type of wave affect its power? No

6. Apply: Sound waves are longitudinal waves that can travel through air. Would you expect sound waves to
travel faster through a low-density gas (such as helium) or a higher-density gas such as carbon dioxide?
Justify your answer based on what you have learned.

A low density gas because it requires less power to travel through.

7. Apply: As ocean waves approach the shore, friction with the ocean bottom causes them to slow down. If
the frequency is the same, how will this affect the wavelength of the waves?

I would assume it also decreases.

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 Get the Gizmo ready:
Activity C:
● Click Reset. Select Combined waves.
Combined waves ● Set Amplitude to 10.0 cm, Frequency to 0.75 Hz,
Tension to 2.0 N, and Density to 1.0 kg/m.

Question: What does wave motion look like when transverse and longitudinal waves are combined?

1. Observe: Click Play. Observe the motions of the hand and of the green dot in the middle.

A. What is the motion of the hand? Back, forth, up, and down.

B. Deselect the Lights On checkbox. What is A circle

the motion of the green dot?
In a combined wave, the motion of the medium is circular. So, each point of the spring
moves in a circle as the wave is transmitted from left to right.

C. Click Pause. Compare the crests (high The crests are rounded while the
points) to the troughs (low points). What do troughs are pointed.
you notice?

Combined waves, such as ocean waves, do not look exactly like transverse waves. In the
Gizmo, the troughs are pointy and the crests are rounded. In the ocean, the crests are
relatively pointy while the troughs are rounded.

2. Measure: Click Reset. Select Lights on and Show rulers. Set the Frequency to 1.0 Hz. Check that the
Tension is 2.0 N, the Density is 1.0 kg/m, and the Amplitude is 10.0 cm.

A. Measure the horizontal distance between 150 cm

two crests. What is this distance?

B. What is the distance between two troughs? 140 cm

C. How do the wavelength, wave speed, and It is half of the power even though the
wave power of the combined wave compare settings are the same.
to a transverse wave with the same
settings? Explain.

D. Why do you think the combined wave is I think the combined wave is more
more powerful than either the transverse or powerful than the longitudinal wave.
longitudinal wave with the same amplitude,
frequency, tension, and density?

Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved