Guitar Waves

Kulak, Tim Thornwood High School

Objectives 1. Analyze wave patterns of guitar notes, chords, and groups. 2. a. Relate wave characteristics to sound and wave shapes. b. Relate wave definitions to sounds heard and seen. 3. Illustrate how fixed end strings can vibrate in a number of modes. 4. Prove that the wave pattern of a vibrating string is the superposition of harmonics. 5. Discover factors that control the pitch of a vibrating string. 6. Measure and compare ratios of string lengths for harmonious notes. 7. Convert acoustical signals into electrical impulses electromagnetically. (Optional: Piezoelectrically.) 8. Optional: Observe and analyze wave patterns for processed signals. Apparatus Needed Cassette player, connecting cords (Coaxial one end with bare wires), Oscilloscope, long spring, "Duotone Guitars" (call for plan), cylindrical alnico magnets, copper coils or wire, Wave generator (Thornton), computer program on wave superposition, Video: "Donald in Mathemagicland". Optional: These may be "solicited" from students: Acoustic guitar, electric guitar, small amplifier, various signal processors. Recommended Strategy 1. Play a cassette of a dynamic rock guitar song into an oscilloscope (Heart: "Crazy On You", Led Zeppelin: "Ramble On", etc.) 2. Chart the relationships between wave characteristics (amplitude, wavelength, frequency, etc.) and what is heard and seen. 3. Run wave generator into speaker and oscilloscope to complete and reinforce this chart. 4. Illustrate standing wave harmonics with long spring. 5. Run computer program on superimposing standing waves to show resulting wave forms. 6. "Duotone" guitar experiment: a. Two-string "guitars" have one-meter long strings with metric tape from bridge to nut. b. Tune both strings to the same note on each guitar. c. "Fret" one string at various lengths to produce harmonious notes; record each length as a decimal. d. Create a "group" chord by using each guitar to play a separate note of the chord. Record these string lengths. e. Transform decimal ratios into simple fractions using a student- generated chart. 7. Show intro section of video "Donald in Mathemagicland" dealing with Pythagorean string length ratios to validate experiment. 8. Relate ratios to musical intervals. 9. a. Place magnets into copper coils to form a "pickup". b. Input ends of wire into oscilloscope and/or amplifier. c. Place pickup near a vibrating string and observe. 10. Optional activities: a. Illustrate musical moods with various guitar chord intervals. b. Observe sounds from different electric guitar pickups and relate to standing wave harmonics. c. Observe processed guitar signals to see and hear what is being done with the waves. *d. Run computer Fourier analysis on any of the above!
(See Bill Blunk and/or Art Schmidt.)
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