Resonance (Diane Fisher)

Title: Relating Resonance to Wavelength

Principle(s) Investigated: Resonance, standing waves, wavelength, pitch, speed of sound

Standards : Physical Science Disciplinary Core Idea PS4A Wave Properties; Crosscutting Concept 2.1 Patterns, 2.2 Cause and Effect; Science and Engineering Practices 1.1 Asking questions, 1.3 Planning and carrying out investigations, 1.4 Analyzing and interpreting data, 1.5 Mathematics and computational thinking, 1.8 Obtaining, evaluating, and communicating information.

Student prior knowledge: Students should understand that sound is a compression wave that travels through a medium, and should have been introduced to the concept of a standing wave. They should know the terms wavelength, frequency, node, and antinode, and understand the relationship between wavelength and frequency.

Quickwrite

Materials: "Boomwhackers" musical percussion tubes, assorted tuning forks (some with equal or higher frequency than the boomwhackers), deep containers of water, rulers; for the optional kazoo activity, straws and scissors will be needed.

Procedure: Give each group two boomwhackers. Have them gently strike the boomwhackers and compare the pitch of their tones. The shorter boomwhacker will give the higher tone. Students can also place one boomwhacker near each ear and listen to the tone as you might listen to a seashell. There should be a gentle roaring like the ocean as the ambient noises in the room that are the same frequency as that boomwhacker are amplified as the boomwhacker resonates. Introduce the concept of fundamental frequency with the Feynman story below.

Next, strike a boomwhacker and have students note the tone. Show them a diagram of the standing wave created in the tube:

Be sure they understand that there is a node in the center of the tube and an antinode at either end because the ends are open so the air becomes less compressed. This amounts to only half a wavelength. (Extend the wave lines outside the tube to show them the remainder of the wave so they can see this is so). If we're working with the high C boomwhacker, we now have a rough measure of the length of a C sound wave with a frequency of around 512 Hz.

Now place a cap on one end of the boomwhacker and have the students predict what will happen to the pitch when we strike it again. The answer is in the diagram below. There is now a node at the capped end and an antinode at the open end. The length of the sound wave has doubled and we will go down an octave because lower frequencies have lower pitch. Compare the pitch of the capped high C with the open middle C.

This is what the water's for! Place the end of an uncapped tube into the water, which closes the end of the tube. Then strike a tuning fork and hold it at the opening of the tube. Slowly lower the tube into the water until the length of the tube is correct to resonate with the tuning fork. Measure the length of the tube above the water at the resonance point, and record the frequency and note of the tuning fork.

Each group should enter these values into a data table and multiply the lengths by four to give us our wavelengths. Each boomwhacker's note and length should be recorded as well, to give another measure relating frequency (which we read off the tuning forks) and wavelength (which we measure from the boomwhackers and multiply by two). These can be compared with the frequencies of the tuning forks to relate frequency, pitch, and wavelength. If desired, the speed of sound can be calculated from the equation

Data quickwrite

Open ended tubes

Close ended tubes (in water)

Questions & Answers:

1) During a thunderstorm, you count 3 seconds between the flash of lightning and the thunder. Based on your experimental results today, how far away is the lightning?

2) Both light and sound travel in waves. However, light can travel through a vacuum and sound cannot. Why?

3) Elephants can hear and produce sounds with much lower frequencies than we can, allowing them to communicate across long distances (many kilometers), especially if the infrasonic waves travel through the ground rather than the air. Prior to the 2004 earthquake and tsunami in the Indian Ocean, the elephants in the area fled to higher ground hours before humans were aware of any danger. Can you propose a possible scientific explanation for this?

Applications to Everyday Life:

1) The following comes from a Popular Science article "My Mother, The Scientist" (2002, May 1) in which Charles Hirschberg remembers his mother, the physicist Joan Feynman:

My mother taught me about resonances when I was about 12. We were on a camping trip and needed wood for a fire. My brother and sister and I looked everywhere, without luck. Mom spotted a dead branch up in a tree. She walked up to the trunk and gave it a shake. "Look closely," she told us, pointing up at the branches. "Each branch waves at a different frequency." We could see that she was right. So what? "Watch the dead branch," she went on. "If we shake the tree trunk in just the right rhythm, we can match its frequency and it'll drop off." Soon we were roasting marshmallows.

2) The Tacoma Narrows bridge was a mile-long suspension bridge crossing Puget Sound. It collapsed due to "aeroelastic flutter" produced when the wind blew. The vibrations caused by the wind hit the resonance frequency of the bridge and it shook itself apart in a 42 mile per hour wind just four months after it opened.

3) Similarly, the sometimes spotty distribution of earthquake damage within a given area may have to do with the earthquake matching the resonance frequency of certain structures and as a result, destroying these while leaving others intact.

4) But resonances cause more pleasant effects as well. When you hear the ocean in a seashell, then compare the sound to another seashell, you will probably find they have two distinct tones. Each seashell resonates with the ambient noise that matches its fundamental frequency. Unless they share the same fundamental frequency, they will sound quite different.

5) The exercise we did today with resonating tubes is how brass instruments and organs create their sounds. All acoustic instruments resonate in predictably variable ways to produce their music.

6) In fact, we couldn't hear these nicely resonating instruments were it not for the resonance of the hair cells within our cochlea in the inner ear.

For some really well-done and clearly explained Physics of sound and music, (as well as a lot more great Physics) see:

http://www.physicsclassroom.com/class/sound

Extensions: If time allows, make a straw kazoo! (You will not be very popular with your colleagues that day.)