Wave on a string answer key

Wave on a String

Objective: To observe and manipulate the various properties of waves using an interactive simulation of a wave on a string.

Background: Review the topic Nature of Waves in Chapter 6 of The Sciences

Instructions:

1. It is recommended that you PRINT a hard copy of this entire document, so that the experiment instructions, data tables, and questions may be easily referred to and completed while running the simulation.

2. Download the Wave On a String Answer Sheet from the course website. Enter your data values and question answers into the answer sheet file. Put your NAME on the answer sheet where indicated. Save your completed answer sheet on your computer.

3. SUBMIT ONLY the completed answer sheet, by uploading your file to the digital drop box for the assignment.

Introduction to the Simulation

1. After reviewing the background information for this assignment, go to the website for the interactive simulation

“Wave on a String” at http://phet.colorado.edu/en/simulation/wave - on - a - string . Click the play button on the icon image to run the simulation.

2. Get oriented to the simulation by exploring and manipulating all of the possible variables and options:

MODE: Manual, Oscillate, Pulse. In Oscillate and Pulse modes, you can pause/play and step, and also change other settings regarding the wave characteristics:

AMPLITUDE: 0 to 1.25 cm

FREQUENCY: 0 to 3.00 Hz

DAMPING: None to Lots

TENSION: Low to High

END: Fixed, Loose, or No End

RULERS: display (box checked) or not (box unchecked). When displayed, you will see two rulers, one horizontal and one vertical.

TIMER: display (box checked) or not (box unchecked); start/pause/reset

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).

While 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.

Once you are oriented to how the simulation works, conduct the following four (4) short experiments. As you conduct the experiments and collect data, fill in the data tables and answer the questions at the end of this document.

Experiment 1: Manipulating a Wave on a String

1. Set Up: For this experiment, set the MODE to manual, the DAMPING to None, and the TENSION to high.

2. Procedure:

a. Set the End to NO End. Wiggle the wrench up and down at varying speeds and over various distance ranges. Observe the differences in the properties of the waves produced for varying wiggle action. After wiggling for several seconds, let go of the wrench and observe what happens.

b. 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, set the speed to “slow motion”, and observe what happens.

c. Click “Restart” and set the speed back to “Normal”. 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, set the speed to “slow motion”, and observe what happens.

d. Answer the six (6) questions for Experiment 1 on the Questions page.

Experiment 2: Measuring Wavelength

1. Set Up: Click “Restart”. Set the MODE to Oscillate, set the AMPLITUDE to 0.50 cm, Set the FREQUENCY to 1.00 Hz, set the DAMPING to None, set the TENSION to high, set the END to No End, and display the RULERS. For this experiment, we will be changing the FREQUENCY setting.

2. Procedure

a. After observing the generated waves with the oscillation wheel turning, hit the PAUSE button.

b. Measure the wavelength in centimeters (cm), by using the horizontal ruler to measure the horizontal distance between consecutive wave crests (highest part of the wave) or between consecutive wave troughs (lowest part of the wave). In data table 2, fill in the wavelength value for this frequency setting.

c. Change the FREQUENCY setting to 2.00 Hz. Repeat steps a and b.

d. Change the FREQUENCY setting to 3.00 Hz. Repeat steps a and b.

e. Answer the two (2) questions for Experiment 2 on the Questions page.

Experiment 3: Observing Effects of Tension and Damping on Amplitude and Wavelength

1. Set Up: Click “Restart”. Set MODE to Oscillate, set AMPLITUDE to 1.00 cm, set the FREQUENCY to 1.00 Hz, set the DAMPING to None, set the TENSION to Low, END to No End, and open the RULERS. For this exercise, we will be changing the Damping and Tension settings.

2. Procedure

a. After the oscillation wheel has turned several times, observe the form of the wave that is produced.

b. Click the PAUSE button. Measure the wave amplitude in centimeters (cm), by using the vertical ruler to measure the vertical distance from the reference line to either the wave crest or trough that is closest to the oscillator. Measure the wavelength of the first full wave that is closest to the oscillator, using the same method as in experiment 2 (step 2b). Enter the amplitude and wavelength values in the appropriate boxes in table 3.

c. Click the PLAY button. Gradually slide the Damping setting from None to Lots. Observe how the amplitude, wavelength, and shape of the wave along the string change as the damping is increased.

d. With the damping setting in the Lots position, repeat step b.

e. Click the PLAY button. Change the Damping setting to None and let the oscillation wheel turn several times. Then, gradually slide the Tension from Low to High. Observe how the amplitude, wavelength, speed, and shape of the wave along the string change as the tension is increased.

f. With the tension setting in the High position, repeat step b.

g. Click the PLAY button. Gradually slide the Damping from None to Lots. Observe how the amplitude, wavelength, and shape of the wave along the string change as the damping is increased.

h. With the damping setting in the Lots position AND the tension setting in the High position, repeat step b. For these settings, it will be a little difficult to accurately measure the wavelength and amplitude.

i. Answer the five (5) questions for Experiment 3 on the Questions page.

Experiment 4: Calculating Wave Frequency

1. Set Up: Set MODE to oscillate, set the AMPLITUDE to 0.50 cm, set the DAMPING to None, set the TENSION to the middle setting between Low and High, set the END to No End, and display both the RULERS and TIMER. Set FREQUENCY to 0.50 Hz. For this exercise, we will be changing the FREQUENCY setting.

2. Procedure

a. With the simulation running, position the right or left edge of the vertical ruler over the SECOND or THIRD (from the left) green dot on the string. You will not be measuring with the ruler, just using it as a reference point for counting waves passing it. Position the timer over the vertical ruler without covering the string as it oscillates. With the ruler and timer in these positions, you should be able to count wave crests passing the ruler and also see the timer. Practice counting wave CRESTS that pass the vertical ruler as the simulation runs.

b. Start the timer, and count the number of wave CRESTS that pass the vertical ruler in 10 seconds. EXACT timing is not critical, just stop counting waves when the timer reaches about 10 seconds. In data table 4, enter the number of waves you counted under “Trial #1” for this frequency setting.

c. Repeat step b for a total THREE (3) trials for this frequency setting, resetting the timer between each trial.

d. Change the FREQUENCY setting to 1.00 Hz. Repeat steps b and c.

e. Change the FREQUENCY setting to 2.00 Hz. Repeat steps b and c.

f. For EACH frequency setting, calculate the average number of waves counted in the 10 seconds, by adding up the three trial values (#1, #2, and #3), and dividing by 3. Enter the averages in the “average” column of data table 4.

g. For EACH frequency setting, calculate the wave frequency by dividing the average number of waves counted in 10 seconds (from step f.) by the time interval (10 seconds). This calculates the number of waves passing a given point per second. Enter the actual frequency values in the LAST column of data table 4.

Note that the corresponding frequency SETTING and calculated frequency should be very close if you did the experiment correctly.

h. Answer the two (2) questions for Experiment 4 on the Questions page.

Data Tables and Questions

Enter the data and the answers to the questions below in the Wave on a String answer sheet file found on the course website. The answer sheet is identical to that below.

Data Tables - Each box to be filled in with a value is worth 2 points.

Data Table 2

Frequency Setting

Measured Wavelength in centimeters (cm)

1.00 Hz

2.00 Hz

3.00 Hz

Data Table 3

Damping

Setting

Tension Setting

Amplitude (cm) of first wave crest from the LEFT

Wavelength (cm) of first full wave from the LEFT

None

Low

Lots

Low

None

High

Lots

High

Data Table 4

Frequency Setting

Time

interval

Number of waves counted in 10 seconds

Average number of waves counted in 10 seconds

Number of waves passing in 1 second

(actual wave frequency)

Trial #1

Trial #2

Trial #3

0.50 Hz

10 seconds

1.00 Hz

10 seconds

2.00 Hz

10 seconds

Questions - Each question is worth 3 points.

Experiment 1

1. Wiggling the wrench simulates ________ waves along the string.

a. longitudinal b. transverse c. sound

2. When the wrench is wiggled, a disturbance is created which causes the string to move up and down, representing________ being propagated in a wave ALONG the string. When the wiggling of the wrench is stopped, the wave ________.

a. energy; dissipates b. matter; dissipates c. energy; is amplified

3. In part a. of the procedure, when the wrench is wiggled faster, the wave frequency ____and the wavelength____.

a. increases; decreases b. decreases; increases c. increases; increases

4. When the wrench is wiggled farther UP and DOWN, the wave amplitude:

a. increases b. decreases

5. When the end of the string is Loose or Fixed we observe ______ taking place.

a. interference b. dissipation c. amplification

6. For the experiments with the different “end” settings, which of the following statements is NOT correct?

a. Energy is conserved when there is No End, but is destroyed with the end Fixed or Loose.

b. With the end Fixed or Loose, multiple waves interact along the string.

c. With No End, a single wave is produced which propagates away from the source without returning.

Experiment 2

1. Comparing the measured wavelengths for each of the frequencies in data table 2, the data shows us that as the frequency increases, the wavelength ______.

a. increases b. decreases

2. Wave speed is the product of frequency and wavelength: Wave speed (cm/s) = Wavelength (cm) X Frequency (Hz). Using the data you collected in experiment 2, the calculated wave speed is closest to which of the following values?

a. 2 cm/s b. 3 cm/s c. 6 cm/s

Experiment 3

1. In comparing the measured amplitudes and wavelengths, I observed that as the damping increases, the amplitude ______ and the wavelength ___________.

a. increases; decreases b. does not change; increases c. decreases; does not change

2. In comparing the measured amplitudes and wavelengths, I observed that as the tension increases, the amplitude ______ and the wavelength ___________.

a. decreases; increases b. does not change; increases c. decreases; does not change

3. Adding damping causes the ________ travelling along the wave to be _____________.

a. matter; amplified b. energy; dissipated

4. Increasing the tension causes the speed of the ________ travelling along the wave to _____________.

a. matter; decrease b. energy; increase

5. In data table 3, compare the measured amplitude and wavelength for the original settings of Damping = None, Tension = Low to that of the other three setting combinations. Which setting combination caused greatest changes to the amplitude and wavelength from that of the original settings?

a. Damping=Lots, Tension=Low b. Damping=None, Tension=High c. Damping=Lots, Tension=High

Experiment 4

1. Based on the definition of frequency, and in reflecting on experiment 4, the frequency units Hertz (Hz) represent:

a. the distance between wave crests or troughs

b. the speed at which the wave travels

c. the number of waves passing a given point per second

2. Based on the definition of wave period (the time it takes one complete wave to pass a given point), and in reflecting on experiment 4, the wave period would be determined by:

a. multiplying the frequency times wavelength

b. dividing the wavelength by the frequency

c. dividing 1 by the frequency, i.e., period = 1/frequency