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**Prior Knowledge Questions**

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

Answer: The buoy will move up and down because the wave will push it. - The two images show side views of ocean waves. How are the two sets of waves different?

Answer: The two images showing the two different sides of the ocean are different because the first image of the wave is higher than the second image of the ocean wave.

**Gizmo Warm-up**

- 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.

Answer: a transverse wave moves from left to right, but the particles inside move up and down. The waves move left to right while the hand moves up and down. - 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.

Answer: In this wave, the hand is moving from the left to the right as well as the wave.

**Questions: How do we measure and describe waves?**

- 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?

Answer: Up and down

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

Answer: Up and down

C. Follow the motion of a single crest of the wave. How does the crest move?

Answer: Left to right - Measure: With the lights on, click Pause. Turn on Show rulers.

A. Use the horizontal ruler to measure the horizontal distance between two crests. What is this distance?

This is the wavelength of the wave.

Answer: 100 cm

B. What is the distance between the two troughs?

Answer: 100 cm

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 Pause. What is the wavelength of this wave?

Answer: 140 cm - 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?

Answer: 40 cm

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

Answer: 20 cm - 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?

Answer: Left to right

B. Turn the lights off. What is the motion of the green dot?

Answer: Left to right

C. Follow the motion of a single compression of the wave. How does the compression move?

Answer: Left to right - Measure: With the lights on, click Pause. Turn on Show rulers.

A. The wavelength of a longitudinal wave is equal to the distance between two successive compressions (or rarefactions). What is this distance?

Answer: 141.4 cm

B. How does this compare to the wavelength of the comparable transversewave? (See your answer to question 2C.)

Answer: The type of wave just changed. - 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?

Answer: 20 cm

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

Answer: 10 cm - 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? This is the period (T) of the wave.

Answer: 2 seconds

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

Answer: 0.5 Hz

**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?

Answer: 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.

Answer:

Adjustment | Effect on wavelength | Effect on wave speed |

Increase amplitude | Stays the same | Stays the same |

Increase frequency | Decreases | Stays the same |

Increase tension | Increases | Increases |

Increase density | Increases | Decreases |

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?

Answer: 125 cm

B. What is the wave speed?

Answer: 100 cm/s

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

Answer: v=fλ

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

Answer: 172.11 cm

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

Answer: It will decrease.

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