PH 105

1
PH 105

• Dr. Cecilia Vogel
• Lecture 16

2
OUTLINE

• envelope
• resonances
• plate
• air
• tunings
• guitar

3
Envelope of Plucked String

• The envelope of a plucked string
• has a rapid ____
• and a longer _____
• no _________
• the harmonic content of the decay becomes ______
  with time.

4
Envelope of bowed String

• The envelope of a bowed note
• has a less rapid ______
• and a quick _______
• Sustain lasts as long as bowing continues
• sustain has fairly _________
• the ______ is similar to decay of plucked string.

5
String Sound

• The sound of stringed instrument
• is due to three factors
• the source of the sound
• resonators
• the method of radiating
• 1) the source of the sound
• determines
• the strings alone very quiet
• produce all harmonics if
• many if

6
String Sound

• 2) resonators
• bridge, front and back plates
• volume of air
• video -- why need washtub?
• 3) the method of radiating
• directly (front plate only)
• through sound hole or f-holes

7
Body Resonances

• Guitar often has ______________
• at about 102, 193, 204 Hz
• many higher resonances
• If a string harmonic matches a resonant freq
• it will be

8
Resonances and Timbre

• Resonances
• make
• This changes the
• which changes the
• Tuning the ________
• affects the
• not just the strings are tuned!

9
Resonances and Timbre

• Examples
• strong _____ resonances in violin
• 2-3 kHz
• enhance
• 10-15th harmonic of G3
• give ______ quality
• strong ____ resonances in guitar
• 100-400 HZ
• enhance the
• fundamental and 2nd harmonic of G3 196
• gives a _____ quality

10
Guitar Strings

• E2, A2, D3, G3, B3, E4
• (12 string has 6 pairs,
• each tuned a _____ higher than previous,
• except EB, which is a ____
• fourth is about ____ ratio, __ semitones
• major third is about ____ ratio, __ semitones
• (4/3)(4/3)(4/3)(4/3)(5/4) almost ___
• 4(500 )400 2400 ______

11
Guitar Strings

• E2, A2, D3, G3, B3, E4
• Can you play F2 on E-string?
• ______ higher
• making the string shorter by factor of 1.05946
• Frets placed about 1/18 distance from the
  previous fret (or nut) to bridge
• fig 10.39

12
Frets

• rule of frets
• place fret at 1/18th of
• length ratio is 18/17 1.0588, about 99c instead
  of 100 c
• almost a
• (1/17.817 more accurate than 1/18)
• measure length of string, distance between frets
• ratio ?
• Why are other frets closer?

13
Timbre Demo

• A-string
• Expect strong
• 110 220 near resonances (fig 10.31)
• play C3 (131 Hz) 1st harm ___, 2nd ___
• G-string
• Expect strong fundamental and 2nd harm?
• 196 Hz and 392 Hz near resonances at 200 400 Hz
  (folk only)
• B-string
• f1 246.94 Hz, ___ and ___ harmonics
• near 250 Hz and 550 Hz resonance of classical

14
Summary

• Vibrations of string,
• fundamental and harmonics,
• drive resonances in
• bridge, plates, air cavity.
• Sound quality of different string instruments due
  largely to tuning resonances.
• rule of 18