physics 1251 the science and technology of musical sound unit 2 session 22 mwf strings: guitar,...

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


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.


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.


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


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


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


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)]


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


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


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


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


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


The tuning pegs change the string The tuning pegs change the string tension.tension.

Tuning PegsTuning Pegs


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


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


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


Vibration Modes of Guitar Body:Vibration Modes of Guitar Body:

Holographic vibration images Holographic vibration images

of Guitar of Guitar bodybody


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


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


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..


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



PluckedPlucked


The jack plucks in one direction, The jack plucks in one direction, then retracts in the then retracts in the

opposite.opposite.


A Hammer Dulcimer or CiboloA Hammer Dulcimer or Cibolo


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


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


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.”


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


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


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


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?


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


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.


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.

physics 1251 the science and technology of musical sound unit 2 session 22 mwf strings: guitar,...

Documents

harmonic f

piano string

fundamental mode f

2n4l v string f n

harpsichord unit

harpsichord slide

waves slide

mwf strings