Physics 1251 The Science and Technology of Musical Sound

1
Physics 1251The Science and Technology of
Musical Sound

• Unit 2
• Session 22 MWF
• Strings Guitar, Harp, Piano and Harpsichord

2
Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Foolscap Quiz
• A piano string that has a mass of 6 grams for
  every meter and has a length of 1.02 m is
  stretched with a tension of 800 N. If the string
  is struck by a hammer, what fundamental frequency
  will you hear?

f 1/(2L) v(T/ µ) f 1/(2?1.02)
v(800/0.006) f 179.0 Hz
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 1' Lecture
• The fundamental frequency of a string is equal
  to the reciprocal of twice the length of the
  string multiplied by the square root of the ratio
  of the tension and the linear mass density f1
  1/(2L) ? v(T/ µ)
• Standing waves on the string are responsible for
  the harmonic series of stringed instruments.
• The details of the harmonic recipe depends upon
  the excitation of the various harmonics.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A musical instrument comprises four
  important components

(1) a mechanical energy source
(2) a frequency generator
(3) a frequency filter
(4) an antenna.
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A stringed instrument uses standing waves on
  a string to provide the frequency generation.

String Standing Waves
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• A Standing Wave results from interference of
  counter-reflecting waves.

Fundamental Mode
f1 vstring / ?1 vstring / 2L
Node
Node
Antinode
?1 /4
?1 /4
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20The distance between neighboring nodes
  antinodes is ¼ ?. N-A d ¼ ?

Second Harmonic
f2 vstring / ?2 vstring / L
Node
Node
Node
Antinode
Antinode
?2 /4
?2 /4
?2 /4
?2 /4
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The Vibrating String Demonstration

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Physics 1251 Unit 2 Session 21 Scales and
Strings

• 80/20Frequency of nth harmonic
• fn 2n/(4L) ? vstring
• fn n/(2L) ? v(T/ µ)

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20The modes that will be present are those
  that are excited.

Energy source can excite selected modes
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20The modes that will be present are those
  that are excited.

Example Guitar Overtones (Harmonics) Plucking,
strumming, damping
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The Guitar is a fretted stringed instrument
• that is plucked or strummed.

Tuning pegs
Neck
Frets
Strings (6)
Body
Bridge
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Density of strings sets range of each string

Denser wire lower pitch
Less dense wire higher pitch
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Frets shorten the string to raise the pitch.

Fret Lo / Ln 1 1.06 2 1.12 3 1.20 4 1.27 5
1.33
Lo
L1
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The tuning pegs change the string tension.

Tuning Pegs
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The strings are attached to the body and sound
  board by a flat bridge.

Bridge
Strings
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20The coupling of the string to the sound
  board will accentuate or attenuate various
  frequencies.

Sound Board and Acoustics filter harmonics
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The response of the body and air cavity
• determine the filtering of the harmonics.

Guitar in cross section
Neck
Truss rod
Sound hole
Bridge
Body
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Vibration Modes of Guitar Body
• Holographic vibration images
• of Guitar body

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harp is a stringed instrument that is
  plucked. Its strings are of various lengths.

Strings
Traditional Irish Harp
Sound Board
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The principal pitch of each string in a Pedal
  Harp is determined by its length.

Pedal Harp
Strings
Pedals
However, depressing a pedal shortens or lengthens
the string length, raising (or lowering) the
pitch incrementally.
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The principal pitch of each string in a Pedal
  Harp is determined by its length.

However, depressing a pedal shortens or lengthens
the string length, raising (or lowering) the
pitch incrementally.
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harpsichord is a keyboard stringed
  instrument whose strings are plucked.
• Each string is used for one pitch only.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harpsichord is a keyboard stringed
  instrument whose strings are plucked.
• Each string is used for one pitch only.

25
Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harpsichord is a keyboard stringed
  instrument whose strings are plucked.
• Each string is used for one pitch only.

26
Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harpsichord is a keyboard stringed
  instrument whose strings are plucked.
• Each string is used for one pitch only.

Harpsichord Action
Damper
Plectrum
String
Jack
Key
27
Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harpsichord is a keyboard stringed
  instrument whose strings are plucked.
• Each string is used for one pitch only.

28
Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Harpsichord is a keyboard stringed
  instrument whose strings are plucked.
• Each string is used for one pitch only.

Plucked
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The jack plucks in one direction, then
  retracts in the opposite.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• A Hammer Dulcimer or Cibolo

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Piano is a keyboard stringed instrument
  whose strings are hammered. Each string is used
  for one pitch only.

Fortepiano
Piano
Strings
Key Board
Sound Board
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The Piano strings are hammered by a felt hammer,
  actuated by the action.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The Piano strings are hammered by a felt hammer,
  actuated by the action.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20A Piano has multiple strings (in the treble)
  to provide a more powerful sound.

Multiple Strings
Sound Board
Bridge
Frame
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Piano strings are tensioned by tuning pins in a
  strong frame.

Frame
Bass Strings
Tuning Pins
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Piano hammers are made of felt and wood.

Hammer Head
Back Check
Wood
Felt
Pivot hinge
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• The timbre of the piano sound is affected by the
  hardness of the hammer felt.

Felt hard or soft?
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20The timbre of a musical instrument is
  determined by the excitation, frequency
  generation, filtering and broadcast of the
  harmonics.

Excitation
f Response
f Generation
Broadcast
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Summary
• fn n/(2L) ? v(T/ µ)
• The node-antinode distance is ¼ ?.
• The timbre of a stringed instrument is determined
  by its harmonic recipe.
• The harmonic recipe of a stringed instrument is
  determined by its mode of excitation, the
  harmonics of a string, and the natural frequency
  response of the instrument.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• Summary
• A Guitar is a stringed instruments with frets
  played by plucking.
• A Harp is a fretless stringed instrument played
  by plucking.
• The Harpsichord is a stringed instrument with
  keys that, when depressed, lift a plectrum that
  plucks one or more strings.
• The Piano is a stringed instrument with a
  keyboard that causes a felt hammer to strike the
  string.