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investigating the relationship between wave speed, wavelength, frequency, and period of waves by uti

PHY112 On-line Lab #8 WAVES

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Instructions: Download and save this document to your computer. Answer the questions directly on this document. When you are done, SAVE the file and return it to your TA via BB Learn. Please contact your TA with any questions or other issues.

Part of this lab asks you to insert a drawing in several places. Please see the Appendix at the end of this document for some simple instructions and suggestions.

You will need to make and insert sketches into this document for the last part of the lab. See the appendix at the end of this document for simple instructions on how to draw and then insert a sketch on the computer. If you have questions or difficulties contact your Lab TA for assistance.

Introduction:

This lab deals with the basic physics of waves. For some of you this may be a bit of review. Though, the discussion here is not primarily about electricity or magnetism, the concepts are important because much of what we know about Electro-Magnetism is based on the study of waves. In fact, the Electro-Magnetic spectrum is made of waves and is an elemental feature of our physical universe. This lab will prepare us for a follow-up lab which will deal specifically with radio wave propagation.

We are surrounded by waves, and while the type of waves can vary, the measurable characteristics of waves can be applied to all, including transverse (e.g. waves on a string) and longitudinal (e.g. sound). Waves obey the wave equation, which states:

That is, the wave speed is equal to the product of the wavelength and the frequency of the wave.

Instructions

Throughout this lab assignment, you will be investigating the relationship between wave speed, wavelength, frequency, and period of waves by utilizing a PhET simulation .

Go to the web page https://phet.colorado.edu/en/simulation/wave-on-a-string.

Click on the Waves on a String icon. This will take you to the following page.

Take a moment to familiarize yourself with how the simulation works. There are three ways to generate a wave on the string: ManualOscillate, and Pulse. There are also three ways to “hold” the end: Fixed EndLoose End, and No End. The controls at the bottom give you the means to control the damping and the tension in the string. When Oscillate is selected, you can control the wave frequency and amplitude. When Pulse is selected, you can control the amplitude and pulse width. When Rulers is selected, you have rulers (which you can drag) and which enable you to measure amplitude and wavelength. When Timer is selected, you have access to a stopwatch (presumably to measure the period of the wave). When Reference line is selected, a horizontal line is available for amplitude comparisons. The Pause button is useful if you wish to freeze the wave to take measurements. Once you are familiar with the controls, reset the simulation and proceed to Task #1.

Task #1

In this task, we are going to investigate the relationship between wavelength, frequency, and wave speed. In the upper left box, select Oscillate. In the upper right box, select No End. In the bottom box, move the Amplitude slider to 1.25 cm, move the Frequency slider to 1.00 Hz, move the Damping slider to None, and move the Tension slider to High. Select Ruler and pause the wave when a full wavelength is visible (crest to crest or trough to trough). Using the ruler, measure the wavelength as accurately as possible. Record your answer in the table below. Repeat the procedure, obtaining and recording wavelengths for all of the listed frequencies in Table 1 below.

Table 1: High Tension

Frequency (Hz) Wavelength (cm) Wave speed (cm/s)
1.00
1.50
2.00
2.50
3.00

Once you have measured all of the wavelengths, calculate the wave speed for each frequency (multiply the frequency by the wavelength). Record your answers in the table.

Questions

1. Move the Frequency slider to 2.00 Hz and select Timer. Start the timer when a crest passes through the window. Allow 20 waves to pass through the window and stop the timer (start your count at zero!). Divide the total time by 20. Show your work. You now have the time it takes for one wave to pass through the window. In other words, you have measured the period. Repeat the procedure for a frequency of 3.00 Hz. Does period appear to be related to frequency? If so how (proportional, inversely proportional, etc.)? If not, why not?

2. Does the wave speed appear to depend on frequency? If so, how (proportional, inversely proportional, etc.)? If not, why not?

3. Move the Amplitude slider to 0.60 cm and select a frequency of 3.0 Hz. Measure the wavelength and calculate the wave speed using the procedure given above. Is the speed you calculated similar to the value in the table? Does the wave speed appear to depend on the amplitude?

4. Calculate the average wave speed (add up all the wave speeds in the table and divide by 5). Briefly explain your work.

5. Write a few sentences summarizing the results of this task.

Task #2

While it may seem from the equation in Task #1 that wave speed depends on both wavelength and frequency, it turns out that it depends on the properties of the medium (the string itself). This sort of behavior is seen in Ohm’s law (from Lab 5). The resistance of piece of wire depends on properties of the wire (length, cross sectional area, and composition), and the current flowing through the wire simply responds to the voltage that is placed across it. Likewise, wave speed along a string is constant for a given string thickness and tension. If we change the tension in the string, we change the wave speed.

Questions

1. Make a prediction as to how wave speed depends on tension. How would increasing the string tension change the wave speed (increase, decrease, remain constant)? Explain your reasoning.

Reset the simulation by using the circular arrow in the lower right corner. In the upper left box, select Oscillate. In the upper right box, select No End. In the bottom box, move the Amplitude slider to 1.25 cm, move the Frequency slider to 1.00 Hz, move the Damping slider to None, and move the Tension slider to the value between Low and High. Select Ruler and pause the wave when a full wavelength is visible (crest to crest or trough to trough). Using the ruler, measure the wavelength as accurately as possible. Record your answer in the table below. Repeat the procedure, obtaining and recording wavelengths for all of the listed frequencies in Table 2 below. Once you have all of the wavelength measurements, you can calculate the wave speed for each frequency.

Table 2: Medium Tension

Frequency (Hz) Wavelength (cm) Wave speed (cm/s)
1.00
1.50
2.00
2.50
3.00

Finally, repeat the entire procedure listed above with the Tension slider set to Low. Record your data in Table 3 below.

Table 3: Low Tension

Frequency (Hz) Wavelength (cm) Wave speed (cm/s)
1.00
1.50
2.00
2.50
3.00

2. Similar to question 4 from Task #1, calculate the average wave speed when the string is under Medium tension (from Table 2 above). Briefly explain your work.

3. Likewise, calculate the average wave speed when the string is under Low tension (from Table 3 above). Briefly explain your work.

4. Compare the wave speed when the string is under High tension (question 4 of Task #1), Medium tension (question 2 from Task #2), and Low tension (question 3 from Task #2). Do the results agree with your prediction?

5. Write a few sentences that summarize the main point of this task.

Task #3

Up to this point, the waves the we have generated have literally been traveling out the window. Let’s see what would happen if we allowed the waves to reflect back to the oscillator.

Note: for a specific choices of frequencies, we can even create standing waves, which appear to remain stationary.

Reset the simulation by using the circular arrow in the lower right corner. In the upper left box, select Oscillate. In the upper right box, select Loose End. In the bottom box, move the Amplitude slider to 1.25 cm, move the Damping slider to a small non-zero value (one tick mark above None), and move the Tension slider to High. We are now able to adjust the frequency to generate a standing wave. The defining features of a standing wave are nodes (places where the string does not move) and anti-nodes (places where the string moves maximally, such as the oscillator and the loose end). What you see now is NOT a standing wave because there are no nodes. This particular configuration (with an anti-node at each end) has similarities to blowing air across an open pipe. The equation that tells us which frequencies will give a standing wave for such a configuration is:

Here, is the wave speed (found in Task 1 and 2 above), is the distance between the oscillator and the pipe which the ring is sliding on (measured along the dashed line), and is a number ().

Questions

1. Use the ruler to measure the distance between the oscillator and the pipe as precisely as possible. Record your value here.

2. The fundamental frequency, also known as the first harmonic, is obtained when . Using the value of wave speed, you calculated when the string was under high tension, calculate the fundamental frequency and record your value below. Set the frequency slider to this value. Wait about 10 seconds for any extraneous oscillations to dampen out, and insert a sketch in the box below, of what the wave looks like. (There should be a node somewhere, but the damping changes things a bit, so you may not see it. However, there should be a region of string that is undergoing significantly less vibration. Take this to be the node.) Indicate on your sketch the location of the nodes (indicate with an N) and antinodes (indicate with an A) of the oscillation. (see the appendix at the end of this document for simple instructions on how to draw and then insert a sketch on the computer)

Insert Sketch here:

3. Multiply the fundamental frequency by 2. This is the second harmonic (also known as the first overtone). Record your value below. Move your slider to this frequency, wait about 10 seconds, and sketch what the wave looks like. (There should now be two nodes, but for reasons similar to before, they may not be readily apparent. Take the regions that are oscillating significantly less as the nodes.) Indicate where the nodes and antinodes are (using the same notation as before). (see the appendix at the end of this document for simple instructions on how to draw and then insert a sketch on the computer)

Insert Sketch here:

4. Multiply the fundamental frequency by 3. This is the third harmonic (or second overtone). Record your value below. Move your slider to this frequency, wait about 10 seconds, and sketch what the wave looks like. As before, indicate the location of the nodes and antinodes.

Insert Sketch here:

5. What frequency is the sixth harmonic? Calculate it and record your value below. What would it look like? Sketch a picture in the box below, indicating where the nodes and antinodes are.

Insert Sketch here:

6. If the string tension were to be increased, would you expect the fundamental frequency to increase or decrease? Explain.

7. If we were working with a Fixed End (instead of a Loose End), the equation that gives the frequencies of the standing waves is slightly modified to

This is similar to blowing across a pipe or bottle that is open at one end and closed at the other. Doing so can cause it to resonate at a specific frequency, making a unique sound.

Make the necessary adjustments in the simulation. Plug in as well as the other needed values to get the fundamental frequency of this setup. Record your value below. Adjust your slider to the fundamental frequency, wait about 10 seconds, and sketch what the wave looks like. Indicate locations of the nodes and antinodes as before

Insert sketch here:

8. The video found at https://www.youtube.com/watch?v=MICCl0ke058 provides a good application of standing waves to organ pipes. Watch it and write a short paragraph summarizing the results of Task #3.

Save this document and return it to your TA via

BB Learn

APPENDIX

Inserting a drawing:

The quickest and easiest way to insert a drawing is to open MS Paint or some other drawing program of your choice and make the required sketch. We are NOT looking for great artistic talent here, just do your best. Once the sketch is completed to your satisfaction, simply select the whole thing and copy it. You can then paste it into the space provided.

Most of you probably already know how to do this, but here are some basic instructions.

Example:

Step 1)

In MS Paint create your drawing:

Step 2) When your drawing is complete, use the Select dropdown menu and choose Select all

Step 3) Now use the Copy icon or (Ctrl +C) to copy your drawing to the clipboard.

Step 4) Finally, return to this MS document, place your cursor in the yellow highlighted answer area located between the brackets, and paste in your drawing using the Paste icon or (Ctrl +P).

Step 5) And its done!

If you find yourself having any difficulties with this part of the assignment,

please contact your GTA for assistance.

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