## Proposed Capstone Project: Sound

Goal: To develop in the student an understanding of the basic principles of sound and an appreciation of some aspects of its visualization, mathematical modeling, and interdisclipinary applications.

Integration: The primary integration is between the physics (waves; physical properties of sound; mechanisms of sound production and detection; conversion between electrical signals and sound with electro magnetic transducers; speed of sound in various media), mathematics (inverse relationships; ratio and proportion; graphs; mathematical description and modeling of sound in the time and frequency domains; periodic functions; principle of superimposition; Fourier theorem), and technology (computer-based graphical analysis and synthesis of sound). In addition, applications to biology, earth science, medicine, and industrial/agricultural/environmental engineering are investigated.

Suggestions for MBL and Field Activities

1. Collect some simple musical instruments, like slide whistles, flutes, tubular chimes, bells, drums, and related noisemakers. Digitize and characterize their sound waveforms and frequency spectra using a sound analysis program on any recent Macintosh or multimedia PC that has a microphone. Use a small portable tape recorder to record various natural and man-made sounds in your environment. Bring the recording back to the lab for analysis. Make these measure ments in both the time and frequency domains and check them for agreement. Assemble data that demonstrates in what way is a loud sound is different from a soft one; a pitched sound from an unpitched one; a high-pitched one from a low pitched one.

2. a) Design the experiment to measure the frequency range of your hearing using an audio generator and headphones. b) Measure the frequency range of the pitched sounds that you can make by whistling, singling, humming, etc. and to the range of natural sounds your recorded above. c) Compare these two frequency ranges and comment on similarities and differences.

3. Measure the reverberation characteristics of various large rooms around campus by using a small portable tape recorder to record the sound of a sharp impulse (e.g. a loud clap or popping a bag or balloon). Bring the recording back to the lab, measure the sound amplitude decay characteristics and relate to measured size of room.

4. Digitize human speech and characterize it in terms of typical frequency range. Characterize the difference between consonant and vowel sounds. Given that the outer ear forms a 2.7 cm long tube closed at one end (the ear drum), what is its resonant frequency? How does this relate to the frequency range of human speech you measured?

5. Measure the frequency of each chime in a set of tubular chimes. Relate the pitch (frequency) to the characteristics of the tube and develop a mathematical model that predicts the tube length needed to play any given musical note.

6. Measure the frequency of each note of the chromatic scale of any musical instrument. Is there a systematic relationship between the position in the scale and the frequencies of the notes? Give one frequency, can you predict the frequencies of the 12 semitones above that note?

7. Measure the Doppler effect. Leave a tape recorder recording on the streetcurb and drive by as fast as you can while holding down your horn and noting your speed. Now repeat at half the vehicle speed. What did you hear in the car? What do you hear on the tape? Digitize the tape and look at the frequency profile of the sound. What happened? Why (think about what is sound?)? How does the vehicle speed affect the recording? Does the Doppler effect observed with light waves also? What is the "red shift" and why is it important in astronomy?

8. Reflection of sound - parabolic dish voice communications. Construct a sound receiver by placing a microphone at the focal point of a parabolic dish reflector (surface of rotation of a parabola) and test its directional characteristics. (cf. Edmund Scientific catalog). Why are parabolic surfaces used in such equipment rather than easier-to-make spherical surfaces?

9. a) Produce a sustained vowel /i/ as in the word "beet" - what is the fundamental frequency (or pitch)? What are the two next highest dominant frequencies (call them F1 and F2)? Repeat for the vowels /a/ ("hod") and /u/ ("who'd"). For each of your vowels, plot F2 vs F1 on linear scales (F1 [200, 900] and F2 [800, 2600]) - this is called the vowel triangle for American English. What distinguishes these vowels? b) Produce the sustained fricatave consonants /s/ ("so"). How does its amplitude and frequency characteristics compare with the vowels? Are any dominant frequency characteristics visible? Try some other sustained fricatave consonants, like /f/ ("five") and /|/ ("show"). How do they compare with /s/ in time and frequency?

10. Refraction - Sound Lens. Fill a balloon with carbon dioxide (CO2). Ask a friend to whisper toward you while moving away. When you can't hear her very well, ask her to stop moving away, but to continue whispering. Now hold the CO2 balloon up to your ear. What do you hear? Why? Repeat with an air-filled balloon. Explain the difference. Make an analogy to optical lenses.

11. Interference - Destructive and Constructive: Place a 500 Hz sound source near the center of an empty room with full walls (a mostly empty room with full walls is desirable, but not mandatory). The sound source combined with reflected sound waves will result in regions where waves interfere destructively (quiet) and constructively (loud). Move slowly around the room and use your ear to find the regions of interference. Draw a map of these regions (show the quiet areas by "Q" and the loud areas by "L") and the room including the walls and any large objects. Do you see any patterns in these regions and any relationship between the configuration of the room and these regions?

12. Wavelength, Nodes and Antinodes: Take a 1,000 Hz (1 kHz) sound source outdoors and direct it toward a smooth hard-surfaced wall several meters away to produce standing waves. What is the wavelength of a 1,000 Hz sound? At what separation would you expect to find nodes in the standing wave pattern? By moving your ear slowly back and forth between the speaker and the wall, find and measure the node (quiet) distances and the antinode (loud) distances.

13. Find a playing field with a set of bleachers with solid risers (the vertical surfaces between the steps). Standing at some distance from the bleachers, make a sharp sound and record the resulting echo returning from the bleachers. How does this echo differ from the reflection from a flat wall?

14. Panpipes. Cut tubes (e.g., wide straws) of the following lengths, close them at the bottom (you could substitute test tubes by adding water to each one to create columns of air equal to the following lengths), and tape them together:

```Tube length (cm)  Sing   Scale
----------------  ----   -----
15.7 (15*)        do     C
13.9 (13.4)       re     D
12.6 (12.1)       me     E
11.8 (11.3)       fa     F
10.5 (10)         so     G
9.4 (8.9)        la     A
8.4 (7.9)        ti     B
7.8 (7.2)        do     C
```
What are the fundamental frequencies of the 8 tubes (assume the speed of sound is 33,136 cm/sec)? (F = c/4L, where c = speed of sound and L = tube length). Do your calculations match those measured on your computer? Is 33,136 cm/sec a good estimate for the speed of sound under your experimental conditions?

15. Develop a mathematical model for the reverberation characteristics of a concert hall in terms of multiple reflections with fixed loss at each reflection by sound absorption, time between reflections related to size of room and speed of sound. Relate the loss at each reflection to the nature of reflecting surface - is there a difference between hard surfaces like stone or ceramic tile, and soft surfaces like rugs, soft furniture and wall hangings, and "acoustic" ceiling tile.

16. How does a loudspeaker work? a. Take apart a cheap loudspeaker and describe its components and operation. b. Connect a 1.5 volt dry-cell battery to a loudspeaker: predict, observe, and explain what happens when the battery is connected and then removed. c. Connect a small loudspeaker to the input of an oscilloscope and explain how it can work as a microphone; d. Connect two small loudspeakers with a long length of twisted pair wire and use it as a telephone or intercom between two separated rooms /("Watson! Come here! I need you!")

17. Use a computer music program (such as ConcertWare) to investigate how a waveform's harmonic structure, amplitude envelope, and frequency modulation (vibrato) effect its sound and musical quality. Have each student in the group create an individual sound, then assign each sound to a different musical part in a (pre-composed) musical composition, and have the computer play the resulting performance.

18.What is the Fourier Theorem and what does it have with sound synthesis and analysis? Use a computer mathematics system such as Mathematica to demonstrates this concept and to investigate the sonic properties of periodic functions.

Questions and investigations:

1. Why did humans evolve with a particular hearing range rather than some other range? The wavelength range of sight is easily explained - human visual range corresponds with the maximum in the sun's spectrum - but what about hearing? Is there a typical frequency range of natural sounds? And why do some animals (e.g. dogs) hear higher frequencies than humans?

2. In what way is male and female speech observably different? Why? Are there perception differences in right- vs left-handed people? Is hearing centered on one side of the brain?

3. How is it possible to record, store, and playback sounds on a computer which basically stores only binary numbers? How many bytes of data does it take to recorded/store one second of human speech? Of monophonic music? Of stereo music?

4. How is it possible for two musical instruments, say, a flute and a clarinet, to play a sustained note at the same pitch (frequency) and at the same loudness (amplitude) and still sound different? In what other way(s) can sound differ other than pitch and amplitude.

5. Bats use sound (echolocation) to locate insects (e.g. moths). Do moths use sound to avoid being eaten?

6. Investigate the field of bioacoustics: sound production and perception by animals; communication and other social and signalling uses of sound by animals, the use of sound by animals for navigation and for sensing both animate and inanimate objects in their environment, acoustic mediation of social interactions and predator-prey behavior, the censusing of animal populations by acoustic techniques, and the relationship between animals and their acoustic environment, including their reaction to man-made sounds.

7. How is sound used in earth science? Investigate applications in seismology; seismic sounding, investigations of the interior structure of the earth; potential impacts of man-made sounds from oceano graphic research; Acoustic Thermometry of Ocean Climate (ATOC); applications in geophysical archaeology.

8. Investigate applications of sound in medicine, such as the ultrasonic diagnostic imaging (sonogram); noise and stress and humans and animals.

9. Investigate applications of sound in industrial/agricultural/environmental engineering, such as the acoustic prediction of meat quality and tenderness; sonic tenderization of beef muscle; ultrasonic detection of defects in manufactured goods; and noise pollution and noise abatement.

References:

1. David M. Rubin, The Nature of Sound and Music, Chapter 2 in The Desktop Musician, McGraw-Hill, 1995.

2. Chapter 1, "The technology of Nature" and Chapter 2, "The Nature of Technology", in The Desktop Multimedia Bible, by Jeff Burger, Addison Wesley, 1993.

3. Peter Ladefoged, Elements of Acoustic Phonetics, Univ of Chicago Press, 1962 (\$6.95 100 page paperback).

4. T. W. Gray and J. Glynn, Chapters 14, 15, and 16 in Exploring Mathematics with Mathematica, Addison Wesley, 1991. (comes with audio/data CD-ROM).

5. Auditory Demonstrations CD, Acoustical Society of America (\$26). Contains 39 experiments on 80 tracks.

6. Dr. Joe Campbell, Johns Hopkins University (jpcampb@afterlife.ncsc.mil)

Web Resources:

Traveling waves occur in many different areas of physics, such as acoustics, optics, and quantum mechanics. This document presents a visual introduction to waves and shows how a number of common and not so common phenomena can be explained through wave superposition.
The Wave Theory of Sound
http://asa.aip.org/pierce.html
Excerpts from Chapter 1 of "Acoustics: An Introduction to Its Physical Principles and Applications" by Allan D. Pierce (published by the Acoustical Society of America)
The Sound of Trigonometry
http://www.weber.edu/MATH/FRANK-WATTENBERG/CONNECTED/before-calculus/trigonometry/soundtrg/learn.htm
Frank Wattenberg, Department of Mathematics, Carroll College. Imaginative and original module on the relationship between sound and trigonometric functions. In addition to the usual text and graphic slements, the document includes Quicktime movies, digital sound bytes, links to Maple and Mathematica notebook files, and graphing calculator programs to download.
Real time Experiments from the Little Shop of Physics
http://129.82.166.181/Experiments.html
Brian Jones, Physics Dept., Colorado State Univ. Experiments you can do right now, right where you are... Innovative collection of simple scientific experiments that can be done right where you sit. Includes a facinating auditory experiment, based on the "circularity of pitch judgement" illusion, using the Shockwave plug-in to create a working on-screen "piano keyboard".
CERL Sound Group

```-------------------------------------------------------------------------
Tom O'Haver                Professor of Analytical Chemistry
University of Maryland     Department of Chemistry and Biochemistry
College Park               Maryland Collaborative for Teacher Preparation
(301) 405-1831             to2@umail.umd.edu
(301) 384-0183             http://www.wam.umd.edu/~toh/toh.html```