Acoustics - PH 105
Spring, 2002
Standing Wave

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.

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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) | How a CD Burner works |
Noise reduction headsets

Date Chpt Topics
Mar. 4 1 Introduction, survey, pictures, what is "sound", definitions of physical quantities (handout)
Mar. 6 2 Vibrations.  Examples, amplitude, frequency, period, spring/mass system, radio frequencies (AM, FM, shortwave - WWV), NIST, pendulum, computer demos, time graph of periodic motion, 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. 8 3 Waves.   definitions of transverse and longitudinal wave, examples, velocity = frequency x wavelength, standing waves, sound waves in air,

    Sound creation with a tuning fork


Two videos: "Longitudinal Waves in a Helical Spring",  #5, I, 3:45  (a) shows how the leading edge of a pulse compresses the medium and the trailing edges expands it. (b) each coil of spring undergoes SHM, (c) two pulses coming from opposite directions pass through each other, momentarily interfering constructively and destructively.  "Longitudinal Standing Waves", #6, I, 5:20 - continuous longitudinal waves are produced by a variable-frequency mechanical driver and are reflected off of the fixed end.  At certain frequencies, the interference produced a standing wave with nodes and antinodes, as illustrated with a strobe (blinking light).  Model: the spring represents a standing sound wave in air and the coils represent air molecules.  Note: vibration nodes = pressure antinodes,  vibration antinodes = pressure nodes.

Mar. 11 3, 4 Sound Waves.  video: "Sources and Propagation of Sound", #1, II, 3:51.  A vibrating tuning fork is examined with a strobe, computer animation, speaker and a "sensitive flame".  Clint Sprott: 1. ringing bell in a vacuum jar, 2. inhale helium,...   then inhale sulfur hexafluoride (density = r = 5 rair ).   The velocity of sound in different media, change of velocity with temperature, Clint Sprott: 3. pipe filled with gas - shows standing sound waves.  Reflection of waves (i = r), refraction of waves, video: "Reflection and Refraction of Waves in a Ripple Tank", #7, I, 3:32. Resonance  of various systems - recall the video with the variable-speed jig saw and the string, tuning fork - in air and on a wooden box.
Mar. 13 3, 8.4 Interference of sound, "Sound Divided into Two Paths of Differing Length", #5, II, 2:52.  One sound source is split into two paths of differing lengths.  Then the sounds paths are brought together and interfere.
Beats - occur when two waves of slightly different frequency are added. Demo: f=440 Hz, f=436 Hz, using two tuning forks.   "Beat Phenomena", #6, II, 3:50.  A beat pattern is produced (a) with two tuning forks of slightly different frequency and (b) with two electronically produced sound waves. 
Diffraction - the property of waves that causes them to bend around obstacles. b = l/s.   "Diffraction of Waves", #8a, I, 2:25 This shows how waves on a ripple tank take a curved path around a barrier. (stop at interference with two bobbers).  "Bending of Sound Waves around an Obstacle", #7, II, 2:45.  This illustrates how sound from a speakers bends around and obstacle and is received by a microphone.
Interference - the combination (or addition) of two waves traveling in the same medium at the same time.  Demo: Pasco wave synthesizer 440Hz + 440 Hz.  "Interference", #8b, I, 2:20.  Two sources of waves on a ripple tank travel outward, overlap and interfere with another, shows places of constructive and destructive interference.  Demo: Tuning fork - rotate. 
Mar. 15 3,4 Doppler effect, "Doppler Effect - Rotating Whistle" #8, II, 1:58.  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.  "Vibrations of a Guitar String" #6, III.  Demos: guitar sound (keyboard), acoustic guitar (Lars Rehnberg).  pages 208-209.
End of material that will be on Test 1.
Mar. 18 3,4

Vibrating air columns: closed tube, open tube, computer demo #1 (local), computer demo #2 - Web, End correction: add )=0.613 R at an open end (R = inside radius of the tube), plastic tube, flue pipes (p. 323), slide whistle, 40-inch organ pipe, 8-foot organ pipe.
Video: "Cork Dust ..." (#1, III, 4:35).  Standing sound waves are revealed by cork dust in a glass tube.  The speaker at one end is driven by a variable frequency generator.  At resonance, the cork dust is stirred up showing the location of the vibration antinodes.  Where the cork dust is not moving, there are vibration nodes.
Video: "Gas Flame" (#2, III, 4:43).  The height of the flames shows the location of the pressure antinodes (max. height).  Note that this is effectively a tube that is closed at both ends.  Return to computer demo #2 - third arrangement - closed at both ends.

Mar. 20 2, 4, 13 Do we need end corrections?  Experiment with a plastic tube 36.4 cm long with an inside diameter of 3.5 cm (measure, calculate), Robert Greenler video: 1. whistle and rubber hose, 2. build-a-sound, 3. recorders - long and short, 4. clarinet  (10:00).
Helmholtz resonator - having fun with bottles.  MufflersRobert Greenler video: 5. resonators - bottles, 6. Pepsi phone, 7. Hummer,  8. mentions bugle, trumpet, French horn, and tuba (5:50).
Mar. 22   Test 1 - topics covered from Mar. 4-15.  See the corresponding review sheet.
Mar. 25 2, 13 Vibrating bars.  Robert Greenler video: vibrating rods, xylophone, Nailolian.  Vibrating plates. 2 dimensional standing waves (lab), Video: "Chladni Plate" (#4, III, 3:22).  Vibrating membranes.  equation, demo.  Drums.
Mar. 27 13 Doumbek drum - Middle Eastern hand drum - goat skin head - description - three basic sounds: DUM, TEK, KA - demo by Lars - music ("Jedeli").  Snare drum - demo.   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.  Listen to a CD (Trinidad Tripoli Steelband).   Bells and carillons, handbells. video: "Resonant Modes of a Vibrating Bell using Holography", III, #5 (3:32).   Cymbals, glass bell, wine glasses, Robert Greenler video: "Glass Harmonica" (6:00).
Apr. 3 5, 6 Hearing - the human ear, sound pressure, power and loudness.  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
Apr. 8 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.
Musician's scale (SSL in sones vs. LL in phons) - see p. 108 and 109.  Handout.


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. 10 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. 12 7, 9 Fourier analysis - opposite of Fourier synthesis.  Fourier theorem...  Video: "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. 15   Test 2 - topics covered from Mar. 18 - Apr. 12.  See the corresponding review sheet.
Apr. 17 9 Pythagorean scale, p. 176.  Just diatonic scale.  Demo: TrueBASIC program.  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. 19 23 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.  Audio tape: (a) "Echo and Reverberation", (b) UCLA reverberation room to test acoustic tiles and other absorbers, anechoic room (one foot walls supported by inner tubes) 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.  Calculations.  Measurement of reverberation time - results for various places on campus, calculation for a classroom.
Apr. 22 23
Sound amplification, precedence effect, ringing, Video: "Tuning of Meyerhoff Hall" (15 min.) - take notes on the various design goals and techniques, outdoor music pavilion - Central Park in New York (handout).
Apr. 24 19
Microphones and Loudspeakers.  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.
Apr. 26 27 Noise reduction headsetElectronic music (handout) - musique concrete, music by animation, computer-composed music (demo - "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).
Apr. 29 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 1 29
Digital Sound File Formats
File extension Description Comments
.mid MIDI - musical instrument digital interface Real Player
(free download)
.wav Windows audio file
Can record with "Sound Recorder" 
or Cool Edit.
Cool Edit
.voc voice file Sound Blaster 
(lab experiment)
 "play" and "vedit"
.mp3 CD quality compressed files various players
(see above)
.nwc design to compose music - can also save
as a MIDI format (.mid) or load a MIDI file.
NoteWorthy Composer
.rmi small sound files Microsoft

Digital Sound Files

  • MIDI sound - (MIDI Information, What is MIDI?) | sample files:  .mid (1, 2, 3)
  • mp3 sound - | sample files:  .mp3 (1, J.S.Bach)
  • Two types of sound files from Windows:  .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.

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 3 10
Playing the violin, Demo: Melissa Soluri,  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), piezoelectric pickup, viola (tuned a 5th below a violin).

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.

May 6   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).

Analysis of speech.  Sound spectrograph, speech spectrogram, demo using Real Player Plus - "sound analyzer": spectrum, spectrogram, waveform, graph - 16 band frequency display.

Speech Production.  Science New article - see below..


Speech Production

  • 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.



May 8

       Handout the review sheet for Test 3.   55 minute NOVA video: "What is Music?"

May 10

  Course evaluation (about 20 min), demo: Mike Whiteside - steel drum that he made from a 55 gallon barrel.  Time available for questions.

 Last update: May 8, 2002