Course:PHYS341/2018/Calendar/Lecture 22

Phys341 Lecture 22: Summary and web references

2018.03.05

Textbook Ch.16

Combination tones

1. String Instruments: Lute Family
   • Etymology: Al-oud (Arabic)
   • Plucked string instrument
   • Resonating body
   • Neck with fingerboard
   • Sound hole (usually)
   • (Not bowed, harps, zithers, keyboard etc.)
   • Soundbox Structure
     • Light shell
     • Sound board and bulbous back (oud, lute, setar, sitar, theorbo etc.)
     • Sound board and flat back, separated by ribs (guitar family)
     • Sound board of light resonant wood (spruce, paulownia etc.)
     • Strong enough to support bridge which connects to the strings
     • Usually has sound hole to radiate lowest frequencies
   • Strong neck/fingerboard
     • Withstand tension of strings
     • Allows stopping of strings with fingers (usually fretted)
     • Tuning mechanism at end of neck
2. Strings: “Mersenne’s Rules”
   • Fundamental frequency rises a semitone (~6%) -
   • If length decreases by ~6% (e.g. stopped with a finger)
   • If tension increases by ~12%
   • If string thinner by ~6%
   • If string material density reduced by ~12%
   • (all else being equal).
3. Plucking mechanism (recap)
   • High partials die away faster than the fundamental
4. Radiation mechanism
   • Sound radiated by sound box at the frequencies of its vibration modes.
   • This guitar cannot radiate much below 100 Hz (lowest string fundamental is 83 Hz).
   • Thin the sound board to lower the frequencies.
   • Cannot go too far or wood cracks! Without a hole the lowest mode is 180 Hz.
   • Hole in the sound board causes coupled oscillations (see diagram) at ~ 100 and 200 Hz.
   • Studies on musicians’ preferences show that the position of the air mode has the most effect on the sound.
   • Lower air mode -> more likely to characterize as “bassy”.
   • Textbook nomenclature: Air mode = Cavity resonance, Wood mode = Body resonance
   • http://acoustics.phas.ubc.ca/musical-instruments/strings/plucked/guitar/
5. The energy chain
   • Energy added by plucking the string goes through four stages that convert it to radiated sound, and at each stage the frequency spectrum is modified:
   • Pluck: potential energy – broad frequency spectrum.
   • String: vibrational energy – picks out harmonic spectrum of string (depends on initial shape of string just before release).
   • Sound box: modifies string spectrum according to spectrum of vibrational modes of sound box. Some harmonics preferentially radiated, some suppressed.
   • Shape of radiated spectrum = timbre of the instrument.
6. The pipa paradox
   • Pipas and yueqins have tiny sound holes.
   • Buried behind the string attachment mechanism.
   • Why?
   • Air mode 50-70 Hz.
   • Can we hear this? If so, the effect is very subtle.
   • Needs double-blind listener study.