Standing Wave - 4th Harmonic

Acoustics - PH 105
Spring, 2003
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
Special items of interest:
  * The new $60,000 Allen organ at St. James Lutheran Church
  * The HANG drum (pronounced "hung") - a hand-played steel drum | history | GU-side and DING-side
  * Sound of a cup - with and without instant coffee

List of experiments

1. Simple Harmonic Motion
2. Oscilloscope
5. Vibrating Strings and Wires
6. Ultrasound
3. Resonance
4. Vibrating Bars and Plates
7. Musical Scales
8. Electronic Music -  Part 1 - Part 2
Date Chpt Topics
Mar. 10 1 Introduction, survey, pictures, what is "sound", definitions of physical quantities (handout)
Mar. 12 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). 

Mar. 14 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 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

Mar. 17 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, 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
Mar. 19 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
Mar. 21 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. Demos: guitar sound (keyboard), acoustic guitar (Jennifer Alfred), pages 208-209.  electric guitar and mandolin (Ammon Paquette), pages 217-219.
End of material that will be on Test 1.
Mar. 24 3, 4 -- Electric guitar (Scott McNees) - page 218
-- 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
Mar. 26 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)
-- demos - tenor flute, flute, piccolo (Suzanne Robins and
Kari Boozell) - p. 264.
Mar. 28   Test 1 - topics covered from Mar. 10-21. See the corresponding review sheet (handout).
Mar. 31 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.
... more
Apr. 2 13 -- demo - snare drum (Jake Polancich) - change the striking technique.
-- demo - cymbals (Jake), pan covers (large, small)
-- bells and carillons (old instruments) - 8 modes, strike note
Apr. 4 13, 5 -- Doumbek drum - Middle Eastern hand drum - goat skin head - description - three basic sounds:  DUM, TEK, KA - demo by Lars Rehnberg
-- demo - glass bell, Video 18 - "Resonant Modes of a Vibrating Bell using Holography", III, #5 (3:32).
-- demo - wine glass, Video 19 - "Glass Harmonica", 6:00.
--  steel drums - "Acoustics of Carribean Steel Drums", lecture by Dr. Thomas Rossing at Augustana on April 6, 2000. Science News article. Demo pan - Java applet - start with D4 and go up the scale.
-- Hearing - the human ear, sound intensity
Apr. 7 5, 6 -- sound intensity, sound pressure, audio tape "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

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.
Musician's scale (SSL in sones vs. LL in phons) - see p. 108 and 109. 



I Sound Intensity W/m2
p Sound Pressure N/m2
SL or LI Sound Intensity Level dB
SPL or LP Sound Pressure Level dB
LL or LL Sound Loudness Level phons
SSL or S Sound Subjective Level sones
Apr. 9 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.
Apr. 14 7, 9

Fourier analysis - opposite of Fourier synthesis. Fourier theorem... Video 20: "Fourier Analysis - Sound of a Trombone", III, #7 (4:14). 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).

Apr. 16   Test 2 - topics covered from Mar. 24 - Apr. 14. See the corresponding review sheet.
Apr. 22
9 Pythagorean scale, p. 176. 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)
16. "Stretched and Compressed Scales", tracks 32 (0:59)
27. "Circularity in Pitch Judgment", track 52 (1:20)

Apr. 23 23 Video 21.  "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 - 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 from last time): 35. "Effect of Echoes", track 70 (1:47).
Graph of reverberation time vs. room volume. 
Apr. 25 23
Went over Test 2.  Calculations of reverberation time. Measurement of reverberation time - results for various places on campus, calculation for a classroom.  Sound amplification, precedence effect, ringing.   Outdoor music pavilion - Central Park in New York (handout).
Apr. 28 19
Video 22.  "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

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.

Apr. 30 27 Baffles and enclosures - Demos: show sound interference (cancellation).   Demo: Speaker systems:  regular portable radio vs. Bose Wave radio (1 meter long resonant air channel on connected to the back of one speaker to effectively amplify low frequencies.

Electronic music (handout) - musique concrete, music by animation, computer-composed music.  Demo on audio tape: - "ILLIAC Suite for String Quartet", composer Lejaren Hiller, mathematician Leonard Isaacson - 1957), computer-played music (Demo - Numerology), synthesized music, Arp Axxe keyboard, comparison of a violin and a synthesizer (handout), ADSR envelope (attack, decay, sustain, release).

May 2 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).
May 5   "Journey to the Moon", Dr. Harrison Schmitt, Apollo 17 astronaut.  Special lecture in room 102.  We joined Dr. Carkner's astronomy class (AS 315) in welcoming Dr. Schmitt to Augustana.  He started with a special 13 minute video that was made on the occasion of the 30th anniversary of his landing on the moon in December, 1972.
May 7 29, 10

Digital Sound Formats

File extension


Links / Comments

.mid MIDI - musical instrument digital interface
    Types of MIDI interfaces (new: USB)
RealOne Player (free download)
.wav Windows audio file
Can record with "Sound Recorder" 
or Cool Edit.

WinAmp (free download)
Windows Media Player
    (Windows XP)

.voc voice file Sound Blaster 
(lab experiment)
 "play" and "vedit"
.mp3 CD quality compressed files
  (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)
.rmi small sound files Microsoft

Digital Sound Files

  • MIDI sound - (MIDI Information, What is MIDI?) | sample files:  .mid (1, 2, 3, 4)
  • mp3 sound - | sample files:  .mp3 (1, J.S.Bach, cut 3)
  • Two types of sound files from Microsoft:  .wav (1, 2, 3, 4, 5, 6, 7)  and  .rmi (1, 2, 3)
  • 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.
  • 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), conclusions, motion of a bowed string.

May 9 10
Playing the violin, Demo: Ammon Paquette, 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).

Digital audio compact discs (p. 509). 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 diffraction grating.  The distance between tracks can be determined from diffraction measurements.

May 12 15
How a CD Burner works. CD-R (record at 250 oC), CD-RW (record at 500-700 oC, anneal or erase at 200 oC).

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.  Demo using Pasco sound sensor - waveshapes, sound spectrum (FFT).

Talking Heads:  Speech Production - research being done at Yale University

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

May 14   Video 23 - "What is Music", NOVA program 
May 16   Course evaluation - Karen Soeken, about 20 minutes

Video 24 - "Measurements of Noise Levels in the Wood Shop".

Digital tape recorder.

Allen 320 Renaissance organ - description, photographs, audio tape

3:00 pm,
May 19
  Test 3.  Material covered from Chapter 9 (Musical Scales) to the end of the course.

 Last update: May 28, 2003