Module 6

What Causes Sound Waves?

Instructor Guide

Robert Culbertson, Scott Surgent, Carlon Ami

Synopsis: This exploration is multifaceted: Students first explore the relationship between the frequency of a wave and the corresponding wave pattern on a length of elastic string. Once students have a (visual) understanding of constructive and destructive intereference, students then generate tones, and using Calculator Based Laboratory (CBL) or a Microcomputer Based Laboratory (MBL), gather data on the frequency, period, and behavior of the waves generated. Students gain insight and understanding behind the nature and characteristics of waves. The relationship between frequency and period, as well as velocity, are explored. As a finale, students calculate the speed of sound with a simple variation of this experiment.

Procedure:The first portion of this experiment involves student exploration, which does not require the use of the CBL or MBL. Students generate waves on a piece of elastic string that is fixed at both ends. Using a Wave Function Generator and a Mechanical Vibrator, students slowly vary the frequency and view the resulting wave patterns. At a certain frequency, the string will vibrate back and forth with a certain maximal amplitude, and become a standing wave, or the 1st fundamental wave (the value of the amplitude is not important in this instance). At integer multiples of this frequency, nodes will appear, and the string will be subdivided into smaller standing waves.

Students will also (hopefully, via exploration), determine that at half-way points between the frequencies of the fundamental waves, the string seems to be perfectly flat. This is an excellent, hands-on approach to exhibiting the constructive and destructive behavior of waves.

Once a student has an idea how the waves are behaving on the piece of string, the student moves to the next phase of the exploration, which involves use of the CBL or MBL units. The microphone probe is used, and placed at one end of a length of tubing. A speaker, hooked to the Wave Function Generator, is placed at the other end of the tubing, and a tone is produced and detected by the microphone. The TI-83 calculator or computer then produces a sinusoidal curve representing the tone. Students can determine the time (in msec) of one period of the tone, for a wide variety of tones. Plotting the period vs. the known frequency, an obvious inverse proportion between period and frequency should be evident.

In the last part of the experiment students determine the speed of sound. To do this, place the microphone at one end of the tube, and block the other end of the tube. Snap your fingers at the end with the microphone, and view the pattern on the curve displayed on the TI-83 viewscreed or the computer monitor. An echo should be evident in the graphical display. This process should be repeated with a series of tubes of varying lengths. Guide students to record the length of the tube, and the time between echoes. Students can then make plots of distance the sound traveled down the tube and back to the microphone (2 times the length of the tube, since the sound needs to travel down and back the length of the tube) vs. time. A linear relation should be evident, and the students can perform curve fits to their graphed data. The slope of the distance vs. time graph should be close to the speed of sound in air.

Suggested time: Two class periods.

1. To protect the equipment, you may want to monitor and guide students initially in using the wave function generators and the mechanical vibrators. Once students are aware of the restrictions on the units, they should be able to self-direct rather easily.
2. As the students are generating the 1st, 2nd, etc. fundamental waves, you may want to discreetly ask them if they notice a pattern with the number of waves and subwaves and the generating frequencies. Why do the waves seem to stay in place? At some frequencies, why does there seem to be a flat string? Where are the waves, and what are they doing to one another?
3. The term frequency seems to be unavoidable, even early on. You may want to discuss the term, and illustrate via a simple demonstration.

Term Introduction:

1. Frequency should be mentioned very early, as a basis for the students. Students should be able to understand what is meant by frequency with the elastic string exploration. While the students are performing this exploration, you may also wish to discuss what is meant by a node (ask them to define it in their own terms). Once this first exploration is complete, discuss the idea of constructive and destructive wave interference. It is hoped that the students will come to their own conclusions by viewing large amplitudes and standing waves (constructive interference) and small amplitudes and a seemingly flat string (destructive interference).
2. The second phase of the experiment, where the students compare a period length of the wave curve, will help students understand the relationship between frequency and period. By exploration in this part of the experiment, students should discover that the higher the frequency, the shorter the period, and vice-versa. Allow plenty of time for students to experiment, take measurements, discuss the experiment within their groups and record data. Their casual understanding of the inverse proportion between period and frequency should be strengthened by a plot of their data followed by a general class discussion of the results obtained by various groups.
3. (optional) Resonant frequency and amplitude. Every object has a natural resonant frequency, that is, a frequency where it is "most likely" to vibrate in synchronization with an outside frequency source. When this happens, the amplitude is maximized, and the amplitude continues to have local maximizations at multiples of this resonating frequency. The students should simply adjust the knob until they seem to have a sinusoidal curve of greatest amplitude, and continue to explore thereafter. Can they make the connection between the behavior of sound waves in a tube and the behavior of a vibrating string?

Concept Application:

Speed of sound in air. The students will be supplied with four or five tubes of varying length (tubes of half a meter or less are not very good for this activity). The tubes should be blocked at one end (a hand will do). The microphone is placed at the other end, and a sound is created at the open end near the microphone. The wave pattern generated will show an echo. By repeating this experiment about 3-4 times per tube, the students should collect data of distance vs. time (see above) and determine the speed of sound. This activity makes use of one of the simplest kinematics properties known: distance = (velocity)(time), or d = vt. A plot of d vs. t shows v to be the slope, and hence, the speed of sound!

Physics:

• Frequency (Hertz)
• Period
• Wave Interference
• Node
• Resonance
• Amplitude

Mathematics:

• Integer and Rational Multiples
• Inverse Proportion
• Direct Proportion
• Linear Function/Slope

1. Observation
2. Control of Parameters and Variables
3. Inductive Reasoning
4. Deductive Reasoning
5. Formation of Hypotheses/Testing of Hypotheses

1. A student notices that at a frequency of 60 Hz, three nodes appear as part of a standing wave pattern on a piece of elastic string. (a) What is the 1st fundamental wave frequency? (b) What is happening at 37.5 Hz? Explain.
2. A length of tubing seems to resonate (have maximal amplitude) at a tone of a frequency of 420 Hz. How long is the tube? Explain why this occurs.
3. Explain why for a wave pattern, the period and the frequency can never theoretically be zero. What happens to the frequency when the period of a tone is close to zero? Give an example from daily life. What happens to the period when the frequency of the tone is close to zero? Give an example from daily life.
4. When you make a noise in any setting, Do you always generate echoes? Explain why or why not. If no, explain what must be happening to all of the echoes.

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Last modified 12 Aug 1997
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