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Physics 1251 The Science and Technology of Musical Sound. Unit 2 Session 22 MWF Strings: Guitar, Harp, Piano and Harpsichord. Physics 1251Unit 2 Session 22Strings: Guitar, Harp, Piano & Harpsichord. Foolscap Quiz: - PowerPoint PPT Presentation
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Physics 1251Physics 1251The Science and The Science and
Technology of Musical Technology of Musical SoundSound
Physics 1251Physics 1251The Science and The Science and
Technology of Musical Technology of Musical SoundSound
Unit 2Unit 2
Session 22 MWFSession 22 MWF
Strings: Guitar, Harp, Strings: Guitar, Harp, Piano and HarpsichordPiano and Harpsichord
Unit 2Unit 2
Session 22 MWFSession 22 MWF
Strings: Guitar, Harp, Strings: Guitar, Harp, Piano and HarpsichordPiano and Harpsichord
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Foolscap Quiz: Foolscap Quiz: A piano string that has a mass of 6 A piano string that has a mass of 6 grams for every meter and has a length grams for every meter and has a length of 1.02 m is stretched with a tension of of 1.02 m is stretched with a tension of 800 N. If the string is struck by a 800 N. If the string is struck by a hammer, what fundamental frequency hammer, what fundamental frequency will you hear?will you hear?
f = 1/(2L) f = 1/(2L) √(T/ √(T/ μ) μ)
f = 1/(2f = 1/(2‧1.02) √(800/0.006)‧1.02) √(800/0.006)
f = 179.0 Hzf = 179.0 Hz
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
11′ Lecture:′ Lecture:• The fundamental frequency of a string is The fundamental frequency of a string is
equal to the reciprocal of twice the length of equal to the reciprocal of twice the length of the string multiplied by the square root of the the string multiplied by the square root of the ratio of the tension and the linear mass ratio of the tension and the linear mass density:density:
ff11 = [1/(2L)] = [1/(2L)] ‧ √(T/ ‧ √(T/ μ)]μ)]
• Standing waves on the string are responsible Standing waves on the string are responsible for the harmonic series of stringed for the harmonic series of stringed instruments.instruments.
• The details of the harmonic recipe depends The details of the harmonic recipe depends upon the excitation of the various harmonics.upon the excitation of the various harmonics.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A musical instrument comprises A musical instrument comprises four important components:four important components:
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~
(1) a mechanical energy source; (1) a mechanical energy source;
(2) a frequency generator; (2) a frequency generator;
(3) a frequency filter; (3) a frequency filter;
(4) an antenna.(4) an antenna.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A stringed instrument uses A stringed instrument uses standing waves on a string to standing waves on a string to provide the frequency generation.provide the frequency generation.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~String Standing String Standing
WavesWaves
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
A Standing Wave results from interference A Standing Wave results from interference of counter-reflecting waves. of counter-reflecting waves.
L = L = 22/₄/₄ λλ11
λλ1 1 /4/4 λλ1 1 /4/4
Fundamental ModeFundamental Mode ff11 = v = vstringstring / λ / λ1 1 = v= vstringstring / / 2L 2L
NodeNode NodeNode
AntinodeAntinode
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20The distance between neighboring The distance between neighboring nodes & antinodes is ¼ λ. [ “N-A d = ¼ nodes & antinodes is ¼ λ. [ “N-A d = ¼ λ” ]λ” ]
NodeNode NodeNode NodeNode
AntinodeAntinode AntinodeAntinode
λλ2 2 /4/4 λλ2 2 /4/4 λλ2 2 /4/4 λλ2 2 /4/4
L = L = 44/₄/₄ λλ22
Second Second HarmonicHarmonic
ff22 = v = vstringstring / λ / λ2 2 = v= vstringstring / / L L
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The Vibrating String DemonstrationThe Vibrating String Demonstration
Physics 1251Physics 1251 Unit 2 Session 21Unit 2 Session 21Scales and StringsScales and Strings
80/2080/20Frequency of nFrequency of nthth harmonic: harmonic:
ffnn = [2n/(4L)] = [2n/(4L)] ‧‧ v vstring string
ffnn = [n/(2L)] = [n/(2L)] ‧ √(T/ ‧ √(T/ μ)]μ)]
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20The modes that will be present The modes that will be present are those that are excited.are those that are excited.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~Energy source can Energy source can
excite selected modesexcite selected modes
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20The modes that will be present The modes that will be present are those that are excited.are those that are excited.
Example: Guitar Overtones Example: Guitar Overtones (Harmonics)(Harmonics)
Plucking, strumming, dampingPlucking, strumming, damping
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The The GuitarGuitar is a fretted stringed is a fretted stringed instrumentinstrument
that is plucked or strummed.that is plucked or strummed.
NeckNeck
BodyBody
Strings (6) Strings (6)
Tuning pegsTuning pegs
BridgeBridge
FretsFrets
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Density of strings sets range of each Density of strings sets range of each
stringstring
Denser wire: lower Denser wire: lower pitchpitch
Less dense wire: Less dense wire: higher pitchhigher pitch
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Frets shorten the string to raise the Frets shorten the string to raise the pitch.pitch. LL
oo
LL11
Fret Fret LLo o / L/ Lnn
11 1.061.0622 1.121.1233 1.201.2044 1.271.2755 1.331.33
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The tuning pegs change the string The tuning pegs change the string tension.tension.
Tuning PegsTuning Pegs
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The strings are attached to the body The strings are attached to the body and sound board by a flat and sound board by a flat bridgebridge..
BridgeBridge
StringsStrings
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20The coupling of the string to the The coupling of the string to the sound board will accentuate or sound board will accentuate or attenuate various frequencies.attenuate various frequencies.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~Sound Board and Acoustics Sound Board and Acoustics
filter harmonicsfilter harmonics
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The response of the body and air The response of the body and air cavitycavity
determine the filtering of the determine the filtering of the harmonics.harmonics.
BridgeBridgeSound holeSound hole
Truss rodTruss rod
BodyBody
NeckNeckGuitarGuitarin cross sectionin cross section
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Vibration Modes of Guitar Body:Vibration Modes of Guitar Body:
Holographic vibration images Holographic vibration images
of Guitar of Guitar bodybody
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A A HarpHarp is a stringed instrument is a stringed instrument that is plucked. Its strings are of that is plucked. Its strings are of various lengths.various lengths.
Traditional Traditional Irish HarpIrish Harp
StringsStrings
Sound BoardSound Board
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The principal pitch of each string in a The principal pitch of each string in a Pedal Pedal HarpHarp is determined by its length. is determined by its length.
Pedal HarpPedal Harp
However, depressing a pedal shortens or lengthens the However, depressing a pedal shortens or lengthens the string length, raising (or lowering) the pitch incrementallystring length, raising (or lowering) the pitch incrementally..
StringsStrings
PedalsPedals
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The principal pitch of each string in a The principal pitch of each string in a Pedal Pedal HarpHarp is determined by its length. is determined by its length.
However, depressing a pedal shortens or lengthens the However, depressing a pedal shortens or lengthens the string length, raising (or lowering) the pitch incrementallystring length, raising (or lowering) the pitch incrementally..
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A Harpsichord is a keyboard stringed A Harpsichord is a keyboard stringed instrument whose strings are plucked. instrument whose strings are plucked. Each string is used for one pitch only. Each string is used for one pitch only.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A Harpsichord is a keyboard stringed A Harpsichord is a keyboard stringed instrument whose strings are plucked. instrument whose strings are plucked. Each string is used for one pitch only. Each string is used for one pitch only.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A Harpsichord is a keyboard stringed A Harpsichord is a keyboard stringed instrument whose strings are plucked. instrument whose strings are plucked. Each string is used for one pitch only. Each string is used for one pitch only.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A Harpsichord is a keyboard stringed A Harpsichord is a keyboard stringed instrument whose strings are plucked. instrument whose strings are plucked. Each string is used for one pitch only. Each string is used for one pitch only.
KeyKey
JackJackStringStringPlectrumPlectrum
DamperDamperHarpsichHarpsichord ord
ActionAction
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A Harpsichord is a keyboard stringed A Harpsichord is a keyboard stringed instrument whose strings are plucked. instrument whose strings are plucked. Each string is used for one pitch only. Each string is used for one pitch only.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A Harpsichord is a keyboard stringed A Harpsichord is a keyboard stringed instrument whose strings are plucked. instrument whose strings are plucked. Each string is used for one pitch only. Each string is used for one pitch only.
PluckedPlucked
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The jack plucks in one direction, The jack plucks in one direction, then retracts in the then retracts in the
opposite.opposite.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
A Hammer Dulcimer or CiboloA Hammer Dulcimer or Cibolo
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A A PianoPiano is a keyboard stringed is a keyboard stringed instrument whose strings are instrument whose strings are hammered. Each string is used for one hammered. Each string is used for one pitch only. pitch only. StringString
ss
Key BoardKey Board
Sound Sound BoardBoard
FortepianoFortepiano PianoPiano
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The Piano strings are hammered by a felt The Piano strings are hammered by a felt hammer, actuated by the “action.”hammer, actuated by the “action.”
JackJack KeyKey
HammerHammer
String and String and DamperDamper
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The Piano strings are hammered by a felt The Piano strings are hammered by a felt hammer, actuated by the “action.”hammer, actuated by the “action.”
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/2080/20A A PianoPiano has multiple strings (in the has multiple strings (in the treble) to provide a more powerful treble) to provide a more powerful sound.sound.
Multiple StringsMultiple Strings
Sound Sound BoardBoard
BridgeBridge FrameFrame
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Piano strings are tensioned by tuning pins Piano strings are tensioned by tuning pins in a strong frame.in a strong frame.
FrameFrame
Tuning PinsTuning Pins
Bass StringsBass Strings
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Piano hammers are made of felt and Piano hammers are made of felt and wood.wood.
Pivot hingePivot hinge
Hammer HeadHammer Head
Back CheckBack CheckFeltFelt
WoodWood
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
The timbre of the piano sound is affected The timbre of the piano sound is affected by the hardness of the hammer felt.by the hardness of the hammer felt.
Felt –Felt –
hard or soft?hard or soft?
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
80/80/2020The timbre of a musical instrument is The timbre of a musical instrument is determined by the excitation, determined by the excitation, frequency generation, filtering and frequency generation, filtering and broadcast of the harmonics.broadcast of the harmonics.
♩ ♪ ♫♩ ♪ ♫ ff1 1 f f2 2 f f3 3 f f44
fn
~~ ~~ExcitationExcitation
f Generationf Generationf Responsef Response
BroadcastBroadcast
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Summary:Summary:• ffnn = [n/(2L)] = [n/(2L)] ‧ √(T/ ‧ √(T/ μ)μ)
• The node-antinode distance is ¼ λ.The node-antinode distance is ¼ λ.
• The timbre of a stringed instrument is The timbre of a stringed instrument is determined by its harmonic recipe.determined by its harmonic recipe.
• The harmonic recipe of a stringed The harmonic recipe of a stringed instrument is determined by its mode of instrument is determined by its mode of excitation, the harmonics of a string, excitation, the harmonics of a string, and the natural frequency response of and the natural frequency response of the instrument.the instrument.
Physics 1251Physics 1251 Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord
Summary:Summary:• A Guitar is a stringed instruments with A Guitar is a stringed instruments with
frets played by plucking.frets played by plucking.
• A Harp is a fretless stringed instrument A Harp is a fretless stringed instrument played by plucking.played by plucking.
• The Harpsichord is a stringed instrument The Harpsichord is a stringed instrument with keys that, when depressed, lift a with keys that, when depressed, lift a plectrum that plucks one or more strings.plectrum that plucks one or more strings.
• The Piano is a stringed instrument with a The Piano is a stringed instrument with a keyboard that causes a felt hammer to keyboard that causes a felt hammer to strike the string.strike the string.