Fourier synthesis - 10 harmonics

Acoustics - PH 105
Winter, 2004-2005
Vibrations and waves, perception and measurement of sound, musical instruments, the human ear and voice, electrical production of sound, acoustics of rooms, electronic music and environmental noise.
Textbook:  The Science of Sound, 3rd Edition, Thomas Rossing, F. Richard Moore, Paul Wheeler, Addison Wesley (2002).
Instructor:  David R. Renneke, Science 205, 309-794-3403,
Course syllabus (Word document) | class list | videos | bottom of the page
Test 3 - 3:00 pm, Tuesday, Feb. 22. Chapters 9,10,15,16,19,20,23,24,26-29
       List of experiments
1. Simple Harmonic Motion
2. Oscilloscope
3. Resonance
4. Ultrasound

5. Vibrating Strings and Wires
6. Vibrating Bars and Plates

7. Sound Level
8. Musical Scales
9. Electronic Music -  Part 1 - Part 2
     Einstein quotes  |  World Year of Physics 2005  |  The 1905 theories
1. "A table, a chair, a bowl of fruit and a violin; what else does a man need to be happy."
2. "The whole of science is nothing more than a refinement of everyday thinking."
3. "If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music.  I get the most joy in life out of music."
4. "I have no particular talent. I am merely inquisitive."
5. "Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world."
Date Chpt Topics
Nov. 29 1 Introduction, survey, pictures, what is "sound", definitions of physical quantities (handout)
Dec. 1 2 -- Vibrations: examples, amplitude, frequency, period, spring/mass system, radio frequencies (AM, FM, shortwave - WWV), NIST, time of day
-- Pendulum: equation for the period T, demo: 3 different lengths, computer demos (Interactive Physics), time graph of periodic motion, demo: oscilloscope

Later we will return to the other examples in chapter 2:  Helmholtz resonator, drumheads, vibrating bars and plates (xylophone, cymbals).  Also, we will cover the vibration spectrum later (Section 2.7). 

Dec. 3 3 -- Damped vibrations: demo: mass on a spring - friction with air vs. water.
-- Waves:  definitions of transverse and longitudinal wave, demo: examples (clothes line, wave machine, slinky), velocity = frequency x wavelength, (v = f
-- Standing waves: definition, demo:  clothes line, wave machine
-- Sound waves in air: definition, demo: 440 Hz tuning fork, plastic tube (resonant air column), Computer animation (longitudinal waves)

    Sound creation with a tuning fork



Video 1

Dec. 6 3, 4 -- Longitudinal waves - Video 2 
-- Longitudinal standing waves - Video 3
-- Sources of sound (tuning fork, speaker) - Video 4
-- Velocity of sound in different media - air, helium, sulfur hexafluoride - Video 5
-- Change of velocity with temperature, v = 331.5 + 0.61 t, t = Celsius temperature
         demo: two wave machines, two speeds
-- Reflection of waves (i = r), demo: ball, wave machine
-- Refraction of waves - definition - Video 6 - constant f, v and
l change
-- Sound refracts down over a frozen lake, up over a hot highway, up against wind (p. 53)
-- Resonance - definition - e.g. swing, demo: tuning fork - in air and on a wooden box
Dec. 8 3, 8.4 -- Video 7 -  "Sound Divided into Two Paths of Differing Length"
-- Beats: They occur when two waves of slightly different frequency are added.  For sound waves, we "hear" beats (sound waxes and wanes), demo: f=440 Hz, f=436 Hz, using two tuning forks, Video 8
-- Diffraction, Video 9, Video 10
-- Interference, Video 11
Dec. 10 3, 4 -- Doppler effect, Video 12. Two equations - observed freq. f' approaching (higher) ... and observed freq. f' receding (lower).
-- Vibrating strings, demo: vibrator and elastic string, corresponding drawing for 1, 2, and 3 loops. Video 13.  demo: guitar sound (keyboard)
End of material that will be on Test 1.
Dec. 13 4 -- Guitar demonstrations (Katy Wilford, Dennis Dixon), acoustic guitar, pages 208-209.  electric guitar and mandolin, pages 217-219.
-- Vibrating air columns: closed tube, open tube, computer demo (standing waves), Java applet
-- End correction: add 0.613 R at an open end (R = inside radius of the tube)
-- Demos:  plastic tube, flue pipes (p. 323), slide whistle, 40-inch organ pipe, 8-foot organ pipe
-- Video 14 - Standing sound waves are revealed by cork dust in a glass tube.
-- Video 15 - Illuminating gas in a one-meter metal flame tube.  Return to the Java applet - third arrangement - closed at both ends
Dec. 15 2, 4, 12 --  Resonant air column experiment:  plastic tube (La = 36.4 cm, R = 1.75 cm), function generator and a speaker, calculate the effective length (open at both ends), measure the air temperature, calculate the velocity of sound, calculate the fundamental frequency, then measure it and compare.  Repeat the experiment with the tube closed at one end.
-- Video 16 - demos of whistle and a rubber hose, pop bottle, Hummer
-- Cavity (Helmholtz) resonator (p. 67) - a vibrator consisting of a volume of enclosed air with an open neck or port.  Equation to calculate the resonant frequency...
-- Examples: 1. various bottles (p. 263), demo - boiling liquid nitrogen in a singing teakettle, 2. the air cavity in violins and guitars, 3. air cavity in a bass reflex loudspeaker - demo - oscillating flame near the port hole, 4. mufflers (p. 68)
Dec. 17   Test 1 - Chapters 1-3, Sections 4.1-4.3, 8.4.
Jan. 3 2, 13 -- Video 17 - demos of resonators (bottles), Pepsi phone, Hummer
-- Sound of the flute - effect of temperature - increase T, decrease density, increase f, lengthen the tube to compensate (keep it in tune).  Using helium instead of air has the same effect.
-- demo - flute (Betsy Wolin) - p. 262-266.
-- Vibrating bars, demo - tuning fork with f1 = 320 Hz, f2 = 6.25 x f1 = 2000 Hz
-- Tuned bar (two supports), demo - Gamut bells
-- Video 18 - demos of vibrating rods, xylophone, Nailoian
-- Vibrating plates (2 dimensional standing waves)
-- Video 19 - Chaldni plate - p. 33, lab
-- Vibrating membranes, demo - change the diameter and the tension
Jan. 5 13 -- Transverse vibrating bars and rods
      3 vibrating bars (A6 - 1760 Hz, E7 - 2637 Hz, A7 - 3520 Hz), wind chimes, demo
-- Drums - snare drum (p. 288-289), other drums, demo
 Doumbek drum

    Middle Eastern hand drum - goat skin head
    description, size
    three basic sounds:  DUM, TEK, KA
    technique for playing
    local pictures - 2002
-- Djembe drum - description - the three basic sounds are
  1. Open: played near the rim but not on it, fingers together.
2. Slap: played near the rim but further in than opens, fingers open and loose generally, allowing the fingers to ricochet off the skin.
3. Bass:
played almost at the center using the palm of the hand, fingers slightly upturned so not to touch the skin, motion same as bouncing off trampoline.
               demo - Dennis Dixon (instrument from Science 102)
Jan. 7 13 -- demo - cymbals, pan covers (large, small)
-- bells and carillons (old instruments) - 8 modes, strike note
-- demo - glass bell, Video 20 - "Resonant Modes of a Vibrating Bell using Holography", III, #5 (3:32).
-- demo - wine glass, Video 21 - "Glass Harmonica", 6:00.
--  steel drums - "Acoustics of Carribean Steel Drums", lecture by Dr. Thomas Rossing at Augustana on April 6, 2000. Demo pan - Java applet - start with C4 and go up the scale.
--  steel pan - made by Mike Whiteside - making a pan
Jan. 10 5, 6 -- Hearing - the human ear, sound intensity
-- sound intensity, sound pressure, audio demo: "Intensity", decibel scale 

Typical Sound Pressure Levels (SPL) in Decibels (dB) - Other values on page 104.


 noise weapon 85  outboard motor
155  can burn skin 74  vacuum cleaner
145  jet at takeoff 68  normal conversation
128  machine gun 55  office
120  threshold of pain 45  living room
117  loud auto horn 35  library
115  rock band 20  whisper
108  circular saw, motorcycle 10  rustling leaves
95  lawn mower, heavy traffic 0  threshold of hearing
Jan. 12 5, 6 Demo: sound level meter - measure SPL (sound pressure level) in dB.
CD:  The Decibel Scale (1:57), #4 tracks 8-11: Broadband noise reduced in steps of 6 dB, then 3 dB, then 1 dB.  Speech at these distances from the microphone: 25, 50, 100, 200 cm.
Adding sounds of the same frequency and different frequency.


Units   Symbols Description Units
I Sound Intensity W/m2   SPL or LP Sound Pressure Level dB
p Sound Pressure N/m2   LL or LL Sound Loudness Level phons
SL or LI Sound Intensity Level dB   SSL or S Sound Subjective Level sones
Jan. 14 6, 7 -- Masking - the obscuring of one sound by another. Handout.
-- Hearing Loss - an increase of our threshold of hearing at certain frequencies. Handouts: Human audiogram, noise induced hearing loss.  Noise reduction headsets (Bose: $299).
-- Partials - individual simple tones which make up a complex tone.
-- Timbre (or quality) of a sound.
-- Harmonics. CD: "Effect of Spectrum on Timbre", #28 track 53 (1:17).
-- Sound synthesis - page 13.
-- Fourier synthesis - adding harmonics. Demo: Pasco synthesizer.
-- Fourier analysis - opposite of Fourier synthesis.
-- Fourier theorem... Video 22: "Fourier Analysis - Sound of a Trombone", III, #7 (4:14).-
Jan. 17 7

-- Video 23 - "Measurements of Noise Levels in the Wood Shop" (5:50).
-- Using noise to cancel noise - BYU physicist Scott Sommerfeldt quiets fans in computers - article
-- Sounds recorded in lab: 1 (tuning fork, panflute, telephone) - 2 (bottle, tuning fork, saxophone) - 3 - (guitar, trumpet, tuba).
-- Formant of a tone - a frequency band in the sound spectrum where most of the sound is concentrated. CD: "Effect of Tone Envelope on Timbre", #29 tracks 54-56 (2:16).
-- Vibrato - pitch modulation
-- Tremolo - loudness modulation
End of material that will be on Test 2.

Chapter 9. Musical Scales and Temperament. Musical intervals and scales. Consonant and dissonant intervals. Interval names. Major triads - three notes sounded together with frequencies in the ratio 4:5:6 (for example F A C).  Pythagorean scale, p. 176.

Jan. 19 9 Origin of the Pythagorean scale. Just diatonic scale. Demo: TrueBASIC program (narrated audio tape). Equal tempered scale. Interval for adjacent notes = twelfth root of 2 = 1.05946... Intervals expressed in cents. One octave = 1200 cents - corresponding to 12 notes on the scale.
CD (handout): 18. "Logarithmic and Linear Frequency Scales", tracks 34-35 (1:37)
Jan. 21   Test 2 - Topics covered from Dec. 13 to Jan. 17.
Jan. 24 23

CD (handout) 16. "Stretched and Compressed Scales", tracks 32 (0:59)
                    27. "Circularity in Pitch Judgment", track 52 (1:20)
Video 24.  "Audible and Ultrasound Waves", III, #8 (2:51).
Chapter 23. Auditorium Acoustics
.  Sound absorbers. Anechoic rooms. Deere Technology Center anechoic room - photo 1 - photo 2 - photo 3.  Reverberation time - equation: RT = 0.061 V/A.  Reverberation room applications:  to test acoustic tiles and other absorbers.  Anechoic room applications:  used to calibrate microphones, measure acoustic output, and test noisy machinery.
CD (handout): 35. "Effect of Echoes", track 70 (1:47).
Graph of reverberation time vs. room volume.

Jan. 26 23 24 Demo: keyboard and mike - 1200 watt sound mixer used in Science 102 - Mackie 808S, front panel - speaker.  Showed (a) how to increase the reverberation time to correspond to larger rooms, (b) how to add delay time, (c) feedback - high pitch squeal.
Calculations of reverberation time. Measurement of reverberation time - results for various places on campus, calculation for a classroom. Outdoor music pavilion - Central Park in New York (handout).
Jan. 28 24 Sound amplification, precedence effect, ringing.
Video 25.  "Tuning of Meyerhoff Hall" (15 min.) - take notes on the 8 design goals and techniques.
Photos of the ensemble room in Bergendoff Hall: 1, 2, 3, 4, 5, 6
Jan. 31 19
Sound system components.  Transducers (devices that convert energy from one form to another), four microphone types: crystal (piezoelectric), dynamic (moving coil), condenser (capacitor), electret condenser (metalized plastic).  Dynamic loudspeaker, horn speakers.
Baffles and enclosures - Demos: show sound interference (cancellation).   Demo: Speaker systems:  regular portable radio vs. Bose Wave radio (1 meter long resonant air channel connected to the back of one speaker to effectively amplify low frequencies).
Feb. 2 27 Electronic music (handout) - musique concrete, music by animation, computer-composed music.
- "ILLIAC Suite for String Quartet", composer Lejaren Hiller, mathematician Leonard Isaacson - 1957, computer-played music (audio - Numerology), synthesized music, Arp Axxe keyboard, comparison of a violin and a synthesizer (handout), ADSR envelope (attack, decay, sustain, release).
Feb. 4 24 For those who were absent on Jan. 28 - Repeat showing of Video 25. "Tuning of Meyerhoff Hall" (15 min.) - take notes on the 8 design goals and techniques.
Feb. 7 18 Sound synthesis (p. 137) - time graphs, sound spectrum. Filters (p. 409): low-pass, high-pass, band-pass, band-reject. Octave band analyzer, envelope generator (ADSR - attack, decay, sustain, release). Elements of a clarinet, patch for synthesizing a clarinet sound. Noise - white, pink. MIDI - musical instrument digital interface (p. 677).  MIDI Manufacturer's Association (

A MIDI file doesn't contain actual audio data, but rather contains commands that let MIDI-capable synthesizers re-create a specific musical passage.  The MIDI protocol has been used since 1982 as a way for electronic musical instruments (like digital keyboards and sequencers) to communicate with each other.

Computer sound cards typically feature the ability to interpret MIDI files into music.  Since they don't actually contain the music itself, but rather the commands used to re-create music, MIDI files are a lot smaller than audio files like .mp3, .wma, or .wav.   MIDI files are small and manageable enough that it's not uncommon to find them embedded in Web pages.  MIDI files have the .mid filename extension.

Feb. 9 29 10

Digital Sound Formats (glossary | names)

File extension


Links / Comments

.mid MIDI - musical instrument digital interface
    Types of MIDI interfaces (USB interface)
RealOne Player (free download)
.wma Windows media audio
Record via Windows XP
WinAmp (free download)
Windows Media Player
    (Windows XP)
.wav Windows audio file
Record with "Sound Recorder" or Cool Edit.
.voc voice file Sound Blaster (lab experiment)
 "play" and "vedit"
.mp3 CD quality compressed files - how they work
  (MPEG audio layer 3)
various players
 (see above)
.nwc designed to compose music - can also save
as a MIDI format (.mid) or load a MIDI file.
NoteWorthy Composer
 (free Player for .nwc and .mid)
.pls streaming audio (ShoutCast Playlist File)
(e.g.  WVIK  |  WAUG  |  Davidson College)
WinAmp, RealPlayer,
Apple's iTunes, Quicktime

Digital Sound Files

1. MIDI sound - mid files (1, 2, 3, 4)
2. mp3 files (1, J.S.Bach, cut 3)
wav files (1, 2, 3, 4, 5, 6, 7)
4. NoteWorthy Composer - A shareware software music composition and notation processor for Windows.  It allows you to create, record, edit, print, and play back your own musical scores.  The file extension is .nwc.  You can export these files to .mid and you can import .mid files into NoteWorthy Composer.  You can use an external MIDI keyboard for real-time and step-time entry of your music.  The keyboard used in the Musical Scales experiment has a MIDI interface.
5. GigaStudio - A complete sample playback system that uses the power of a Windows PC to create fully-realized audio productions, complete with mixing and effects.  Designed for professionals.

Chapter 10.  String Instruments.  Sound analysis of a tuning fork and a violin, the four strings: G3 (196 Hz), D4 (294 Hz), A4 (440 Hz) and E5 (660 Hz). Special thanks to Amanda Young for playing her violin in lab (Spring 2000) so these sounds could be recorded and analyzed. Parts of a violin, vibrations of a plucked string (snapshot).

Feb. 11 10
The sound of a ringing bell.  Further explanation of the sound and ringing of church bells by Bill Hibberts.  He also provides an excellent, free program called Wavanal (for a PC) that generates the sound spectrum (does a Fourier analysis) of the sound contained in any .wav file.

Conclusions about plucking a string, motion of a bowed string - slip and stick, playing the violin, demo: Amanda Fenton, vibrational modes of the bridge, plate resonance - holographic interferometry (Augustana graduates: Josh Murphy and Craig Schmaus - summer research) poster, vibrations of the violin body (MWR - main wood resonance about 440 Hz), vibration of the air cavity (MAR - main air resonance from 260 to 290 Hz), acoustical characteristics of violins (handout).

Feb. 14 15

CDs - digital audio compact discs (p. 509) (handout). 12 cm in diameter, 782 megabytes of data (74 min of audio), focused laser beam (1.7 micrometer diam.), red light - semiconductor laser (790 nm), read and record speed = 1.25 m/s, variable rotation rate - 500 rpm inside track, 200 rpm outside track, sampling time = 44,100 per second, freq. range 20-2000 Hz, dynamic range - 90 dB, demo - laser beam reflecting off an audio CD, laser beam through a clear CD and a diffraction grating.  The distance between tracks on a CD and lines on a grating can be determined from diffraction measurements.

How a CD Burner works. CD-R (record at 250oC), CD-RW (record at 500-700oC, anneal or erase at 200oC).

Speech production. Human vocal organs, glottal puffs (waveshapes, sound spectrum), resonator, resulting sound (waveshapes, sound spectrum), formants - peaks in the sound spectrum, shape of the vocal tract for various vowel sounds (i, ae, u).  Artificial voice system of Hideyuki Sawada (Kagawa University, Japan) -  voice1  |  voice2

Analysis of speech. Sound spectrograph, speech spectrogram.

Talking Heads:  Speech Production - research being done at Yale University.
Speech synthesis examples -
Collected by Gregor Moehler, a member of the Experimental Phonetics group at the Institute of the Institute of Natural Language Processing (IMS), Univ. of Stuttgart, Stuttgart, Germany.

Science News magazine"Music without Borders" - Science News, April 15, 2000, p. 252.  This is an interesting article about singing birds and musical compositions, e.g. some by Mozart.  Four sonograms are shown at the right: (a) warbler, (b) whale, (c) flute, (d) person.

Sonograms show frequency rising vertically as time progresses horizontally.  Note that sonograms (the term used in this article) are equivalent to "sound spectrograms" as used by your textbook (and many others).  Also notice that the time graph (waveshape) is shown along the top of each of these sonograms.

Here are sound files from this article.  Listen for similarities - 1,2 - 3,4

Feb. 16   Video 26 - "What is Music", NOVA program (55:00)
Feb. 18   Course evaluation - Kelly Atkins, about 20 minutes
Speech recognition in Word - installation - beginner's instructions - demo
Allen 320 Renaissance organ - description, photographs, recording by Tom Robin Harris
Feb. 22   Test 3 - 3:00 pm, Tuesday, Feb. 22. Topics from Chapters 9,10,15,16,19,20,23,24,26-29.
Material covered from Chapter 9 (Musical Scales) to the end of the course.

 Last update:  Feb. 15, 2005