Hands-on Activity What's a Wavelength?

Learning Objectives

After this activity, students should be able to:

• Define wavelength, frequency, amplitude, pitch and node.
• Calculate wavelength and frequency using an equation.
• Relate a wavelength to pitch and frequency.

Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

NGSS: Next Generation Science Standards - Science

Common Core State Standards - Math

International Technology and Engineering Educators Association - Technology

State Standards

Materials List

Each class needs:

• large (2-liter) graduated cylinder
• 3 cm-diameter tube (glass or plastic) the length of the gradated cylinder
• meter stick
• 4 tuning forks of different pitches, and rubber mallet (or shoe sole)
• What's the Wavelength? Worksheet, one per student

Worksheets and Attachments

Pre-Req Knowledge

Ability to do simple mathematical calculations and use a meter stick for measuring A knowledge of waves is helpful, but not required.

Introduction/Motivation

How do we measure sound? We use a volume knob to adjust how loud it is, but what is the difference between these two sounds? (Strike two different tuning forks so students can listen to each. Expect students to say that one is higher than the other.) What do you mean when you say a sound is higher or lower? (Wait for answers and incorporate them into the definition of pitch.) What you mean when you say a sound is high is that it sounds to you like it has a high frequency. Pitch is your perception of the frequency of a sound. But what is frequency?

Frequency is something we can measure. Frequency is how fast the sound is traveling. Which fork has a higher pitch or a faster frequency? The faster the frequency, the higher we think the pitch sounds. (Reason with students until they say the larger tuning fork has the lower pitch and the lower frequency. Ask someone to draw a wave on the board. Then ask how you measure the frequency from what they have drawn. Draw a second wave that is the same overall length but many more crests and troughs.) Which wave has a greater frequency of repetitions? (Answer: The one the teacher drew.) Which would have the higher pitch? (Answer: The same one.) So how do we measure the frequency of these two waves? How many times does each wave repeat? (Possible answers: 4 and 8)

We measure frequency in hertz which is another way of saying reciprocal seconds, which is a fancy way for saying 1/seconds. If I told you that it takes each of these waves 1 second to get from the left side of the drawing to the right side, how many times does each repeat per second? (Possible answers: 4 and 8) So the first wave has a frequency of 4 Hz and the second wave has a frequency of 8 Hz. But how do I measure how many repetitions this wave (strike the tuning fork) does in one second? It is going way faster than 4 Hz. Let's look back at our waves we have drawn. We can get more information from what we have drawn. How long is each wave? (Answer: The same distance.) So the length of the wave does not change the sound, but what distances do change? (Answer: The distance between the peaks/valleys.) We call those highest points crests and the lowest points troughs. The distance from one peak to the next peak is called one wavelength. That distance is the same as the distance from one trough to the next trough. What about the point in between the crest and the trough? Is the distance between two of those the same as well? (Answer: Yes) We call the point that is in between a node. The amplitude of a wave can be thought of as the height. The high point or the crest has positive amplitude and the low point or the trough has negative amplitude, but the point in the middle or the node has zero amplitude. So what can you tell me about the wavelength of each of these waves? (Answer: The first one has a longer wavelength and the second one has a shorter wavelength.)

So having a longer wavelength means that it has a higher or lower pitch? Higher or lower frequency? (Answers: Lower pitch, lower frequency.) Wavelength is inversely proportional to both pitch and frequency. We have an equation that relates wavelength to frequency using the speed of sound (write on the board: c=λυ). Here, c is the speed of sound and, for our purposes, it is the speed in air, 343 m/s (because it travels at different speeds in water or space). We use λ to represent wavelength and it is measured in meters and υ is frequency, which is in 1/seconds. So is it possible to measure wavelength easier than it is to measure frequency? We are going to try and measure the wavelength of a few of these tuning forks today.

Procedure

Background

It is possible to measure the wavelength of sound using a tube closed at one end. By using a tube submerged in water, you can adjust the length of the tube to match the frequency of the sound wave being measured. At the point at which the sound is the loudest, the length of the tube above the water is one-quarter the wavelength. As sound travels down the tube and back out, nodes are created and to make sure the crest of the wave is at the mouth of the tube, you want to align the node at the bottom of the tube or the top of the water.

wavelength = 4 x the distance from the top of the water to the top of the tube

frequency = speed of sound / wavelength

speed of sound in air = 343 meter/sec

Before the Activity

• Gather materials and make copies of the What's a Wavelength? Worksheet.
• Place the tube inside the graduated cylinder and fill with water.
• Practice with different tuning forks to find which is best for students to test.

With the Students

1. Introduce students to the materials and show what happens when you strike the fork and hold it above the pipe.
2. Ask them how they would use this to find out more about the wavelength. List ideas on the classroom board.
3. Ask students to volunteer to come up and test their theories.
4. After discovering that at some height the pitch is the loudest, tell students what they have discovered. The amplitude is the largest and the sound is the loudest when the distance from the water to the top of the pipe is one-quarter of the wavelength. Have all students independently calculate the wavelength of the tuning fork. Once they have calculated the wavelength of the first tuning fork, have them do the same for the other tuning forks.
5. Have students formulate opinions as to the relationship of pitch and wavelength and record that along with the calculations they have done.
6. Provide the equation to relate frequency and wavelength and have students convert each of the wavelengths they calculated to frequency.
7. Provide a list of musical notes with their associated wavelengths and frequencies (see Wavelength and Frequency List) and ask students to assign notes to each of the forks. Have them compare the "calculated" note to the actual note of the fork and comment on the results. If the notes do not agree, students should provide reasons.
8. Given a tuning fork with a specific note, ask students to predict the height at which the tube must be held and have a volunteer demonstrate when all students have finished calculating.
9. Redefine all keywords and reemphasize all important equations.
10. Ask how students might use what they learned today. Have students offer as many applications as possible before suggesting real-world engineering examples. Refer to the Engineering Connection section for examples of engineering applications. Touch on familiar ways students see sound waves and wavelengths in their everyday lives and how engineering designs created those devices.

Vocabulary/Definitions

amplitude: The height of a wave measured from the origin perpendicular to the motion of the wave.

crest: The point at which a wave has its maximum amplitude.

frequency: The number of waves that pass a point per second.

node: The point at which a wave has zero amplitude.

pitch: The perceived frequency of a sound.

trough: The point at which a wave has its minimum amplitude.

wavelength: The distance over which the wave's shape repeats.

Assessment

Pre-Activity Assessment

Questions: Determine students' prior knowledge by asking them questions about waves, wavelengths, frequencies and pitch.

Activity Embedded Assessment

Questions & Oversight: Since students provide the momentum for the lesson, expect them to provide answers to your questions throughout the activity. In addition, circulate the room as students work on completing the What's a Wavelength? Worksheet to assess how they are progressing through the activity.

Post-Activity Assessment

Worksheet: Have students individually complete the What's a Wavelength? Worksheet and turn it in for grading. Review the answers to determine whether students can do the calculations and form relationships between the concepts, as well as define them.

Investigating Questions

What instruments produce the highest/lowest notes? Why?

How do you make a sound louder/softer/higher/lower?

Safety Issues

• If using a glass graduated cylinder or glass tubing, warn students to be delicate with them so they do not break.
• Only strike the tuning forks with a rubber mallet or on the sole of a shoe.

Troubleshooting Tips

It is important to test all of the tuning forks before starting the activity. Some will have frequencies too low such that students will not be able to hold the tube high enough. If students find multiple points at which the sound is louder, discussion may turn to harmonics. If they find a multiple of the wavelengths, the calculations will give them the wrong result, but you can remind students who are familiar with music that notes repeat on a scale.

References

Copyright

Contributors

Supporting Program

Acknowledgements

This digital library content was developed by the University of Houston's College of Engineering under National Science Foundation GK-12 grant number DGE 0840889. However, these contents do not necessarily represent the policies of the NSF and you should not assume endorsement by the federal government.