Course:PHYS341/2018/Calendar/Lecture 22
Phys341 Lecture 22: Summary and web references
2018.03.05
Textbook Ch.16
Combination tones
- 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
- 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).
- Plucking mechanism (recap)
- High partials die away faster than the fundamental
- 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/
- 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.
- 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.