Posted: June 23rd, 2021

Interactive activity wave on a string

  

Objective

Using a simulation, apply the scientific method to investigate the various properties of transverse waves.

Background Reading

Before attempting the activity, review the topic The Nature of Waves in Chapter 6 of The Sciences. Completing the reading is important for you to be able to correctly apply the properties of waves to the experiments performed in this activity.

Introduction to the Simulation

1. After completing the background reading for this assignment, go to the “Wave on a String” simulation on the PhET simulations website at http://phet.colorado.edu/en/simulation/wave-on-a-string. Click the play arrow on the simulation graphic to run the web-based simulation or click DOWNLOAD to run the simulation locally on your device.

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

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

i. Amplitude: 0 to 1.25 cm

ii. Frequency: 0 to 3.00 Hz

iii. Damping: None to Lots

iv. Tension: Low to High

b. END: fixed end, loose end, or no end

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

d. Timer: display (box checked) or not (box unchecked); start/pause/reset

e. 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).

f. Restart button: starts the simulation over for the current settings

g. Reset button (circular button with a circular arrow, on the lower right of the screen): resets the simulation to the default settings

h. Pause button ( I I ): simulation is running when this is showing; press to pause the simulation

i. Play arrow ( > ): simulation is paused when this is showing; press to run the simulation

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.

3. After spending some time experimenting with the simulation, follow the steps below to conduct four experiments. Before beginning, be prepared to write down your observations.

Experiments

Experiment 1: Manipulating a Wave on a String

In this experiment, you will investigate and observe the properties of waves by manipulating a string attached to an energy source.

Before completing the experiment, write down a hypothesis, based on your current understanding after reading the background information for the activity, that makes specific predictions for how the string will react to changes to the energy source and to changes to the end of the string.

1. Experiment setup: Click the Reset button. The Mode will be set to Manual. Set the Damping to None.

2. Experiment procedure:

a. Set the End to No End. Wiggle the wrench up and down at varying speeds and over various distance ranges. As the wrench is wiggled, a wave disturbance is created and the string to moving up and down represents energy being propagated along the string.  Observe how the properties (wavelength, frequency, and speed) of the wave produced changes with the different wiggle action. Write down your observations.

b. After wiggling for several seconds, let go of the wrench and observe what happens. Write down your observations.

c. 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 and observe what happens. Write down your observations.

d. Click Restart. 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 and observe what happens. Write down your observations.

Answer the questions below to help you formulate some results and conclusions for this experiment. You may need to do some additional experimentation to answer the questions.

1. In part a. of the experiment:

a. Based on the definitions of transverse and longitudinal waves (chapter 6), which type of wave – transverse or longitudinal – is being generated along the string? Explain how you determined this.

b. How is the wave frequency and wavelength affected when the wrench is wiggled faster?

c. How is the wave amplitude affected when the wrench is wiggled farther up and down?

2. For which end setting(s) is wave interference taking place? Explain what causes the interference.

3. For which end setting(s) does the energy propagate away from the source without returning? Explain why the energy does not return.

Experiment Results and Conclusions

Based on your observations while performing the experiment and your answers to the questions above, formulate some results and conclusions for how the string will react to changes to the energy source and changes to the end of the string.

Experiment 2: The Effects of Damping and Tension

In this experiment, you will investigate and observe the effects of adding tension or damping to a wave.

Before completing the experiment, write down a hypothesis, based on your understanding after reading the background information for the activity, that makes specific predictions for how adding tension in the string, or damping the energy along the wave, will affect the amplitude, wavelength, and speed of the wave being generated by the oscillator.

1. Experiment setup: Click the Reset button, and then click the pause button ( I I ) so that the play arrow ( > ) is showing. Set Mode to Oscillate, set Damping to None, set Tension to Low, set end to No End, and display the Rulers. You do not need to adjust the frequency and amplitude settings. For this experiment, we will be changing the Damping and Tension settings.

2. Experiment procedure:

a. Click the play arrow. After the oscillation wheel has turned several times, gradually adjust the Damping from None to Lots. Observe how the amplitude, wavelength, and speed of the energy propagating along the string all change as the damping is increased, using the rulers as an aid in determining the relative changes (you do not need to take any measurements). Write down your observations.

b. Repeat the setup in part 1 above.

c. Click the play button. After the oscillation wheel has turned several times, gradually adjust the Tension from Low to High. Observe how the amplitude, wavelength, and speed of the energy propagating along the string change as the tension is increased, using the rulers as an aid in determining the relative changes (you do not need to take any measurements). Write down your observations.

Experiment Results and Conclusions

Based on your observations while performing the experiment, formulate some results and conclusions for how the independent changes made to the damping and tension each affect the amplitude, wavelength, and speed of the wave being generated by the oscillator.

Experiment 3: Measuring Wavelength

In this experiment, you will measure the wavelength of a wave produced along the string for different settings of the wave frequency.

Before completing the experiment, write down a hypothesis, based on your understanding after reading the background information for the activity, that makes a specific prediction for how changing the wave frequency will affect the wavelength.

1. Experiment setup: Click the Reset button. Set Mode to Oscillate, set Amplitude to 0.50 cm, set Frequency to 1.00 Hz, set 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. Experiment procedure:

Construct a table like the one below. Complete the following steps to complete the table. 

a. After observing the generated waves with the oscillation wheel turning, click 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). Write down the wavelength value for this frequency setting in the table.

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

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

   

Frequency Setting

Measured Wavelength in Centimeters (cm)

      

1.00   Hz

 

2.00   Hz

 

3.00   Hz

To check that you performed the experiment correctly, and to validate the correctness of your hypothesis: Multiply the frequency (in Hz = 1/s) by the corresponding wavelength (in cm). Recall from chapter 6 that: Wave speed (in cm/s) = Wavelength (in cm) X Frequency (in Hz = 1/s). You should calculate the same speed, about 6 cm/s, for each of the frequency settings.

Experiment Results and Conclusions

Explain how the data you collected in the experiment validates the relationship between wavelength and frequency for waves traveling at the same speed, as described in Chapter 6. If your data did not validate the relationship, go back and check that you performed the experiment correctly.

Experiment 4: Calculating Wave Period

In this experiment, you will investigate the relationship between wave frequency and wave period, by counting the number of waves passing a given point for a given time interval and performing a calculation.

Before completing the experiment, write down a hypothesis, based on your understanding after reading the background information for the activity, that makes specific predictions for how the period of a wave correlates to its frequency.

1. Experiment setup: Click the Reset button. Set Mode to Oscillate, set Amplitude to 1.00 cm, set Frequency to 1.00 Hz., set Damping to None, leave the Tension on High, set the END to No End, and display both the RULERS and TIMER. For this exercise, we will be changing the Frequency setting.

2. Experiment procedure: 

Construct a table like the one below. Perform the following steps to complete the table.

a. With the simulation running, position the timer above the 3 cm mark on the horizontal ruler. You will be using the 3 cm mark as a reference point for counting waves passing it. 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. With each wave crest that passes, one cycle of the wave has passed.

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.

c. Repeat step b, resetting the timer after each repeat, until you are confident that you are counting the correct number of wave crests passing in 10 seconds. Record this value in the designated location in the table.

d. Change the Frequency to 2.00 Hz. Repeat steps b and c. 

e. For each frequency setting, divide the time interval (10 seconds) by the number of wave cycles passing in 10 seconds. This calculates the amount of time in seconds that is required for each wave to pass a given point, which is defined as the wave period. Record each calculated period in its designated location in the table.

To check that you performed the experiment correctly, and to validate the correctness of your hypothesis: In chapter 6, you learned that the wave period is equal to 1/frequency. So, the inverse of the corresponding frequency setting (1/frequency) and the calculated period should be very close in value.

   

Frequency

Setting

Time Interval

Number of Crests (Wave Cycles) Passing   in 10 Seconds

Wave Period

(10   seconds/number of wave cycles passing in 10 seconds)

      

1.00   Hz

10   seconds

 

2.00   Hz

10   seconds

Experiment Results and Conclusions

Explain how the data you collected and calculations you performed in the experiment validates the relationship between wave period and wave frequency as described in Chapter 6. If your data and calculations did not validate the relationship, go back and check that you performed the experiment correctly.

Activity Submission

1. Create a document containing a report for each experiment. Your document should contain four paragraphs, one for each experiment. 

a. Title each paragraph with the corresponding name for each experiment, as it is stated in the headings for the experiments above (e.g., Experiment 1: Manipulating a Wave on a String).

b. For each experiment report:

i. Clearly and succinctly present your hypothesis for the experiment.

ii. Based on the information prompted for in the experiment’s Procedure and Results and Conclusions section, clearly and succinctly summarize your observations, results, and conclusions for the experiment, and include any data collected and calculations made.

iii. Clearly and succinctly evaluate the correctness of your hypothesis based on the information presented in part ii above.

c. Include your full name and the date you completed the activity at the top of the document.

2. Submit your document (in either .docx or .pdf file format) as instructed in the assignment location within the Canvas course.

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