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UNT PHYS 1251 - mwf22
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Physics 1251 The Science and Technology of Musical SoundPhysics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & HarpsichordSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Physics 1251 Unit 2 Session 21 Scales and StringsSlide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Physics 1251Physics 1251The Science and The Science and Technology of Musical Technology of Musical SoundSoundPhysics 1251Physics 1251The Science and The Science and Technology of Musical Technology of Musical SoundSoundUnit 2Unit 2Session 22 MWFSession 22 MWFStrings: Guitar, Harp, Strings: Guitar, Harp, Piano and HarpsichordPiano and HarpsichordUnit 2Unit 2Session 22 MWFSession 22 MWFStrings: Guitar, Harp, Strings: Guitar, Harp, Piano and HarpsichordPiano and HarpsichordPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & HarpsichordFoolscap 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 HzPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord11′ Lecture:′ Lecture:• The fundamental frequency of a string is equal The fundamental frequency of a string is equal to the reciprocal of twice the length of the to the reciprocal of twice the length of the string multiplied by the square root of the ratio string multiplied by the square root of the ratio of the tension and the linear mass density:of the tension and the linear mass 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 instruments.for the harmonic series of stringed 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 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord80/2080/20A 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 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord80/2080/20A 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 WavesString Standing WavesPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & HarpsichordA Standing Wave results from interference A Standing Wave results from interference of counter-reflecting waves. of counter-reflecting waves. L = L = 22/₄/₄ λλ11λλ1 1 /4/4λλ1 1 /4/4Fundamental ModeFundamental Modeff11 = v = vstringstring / λ / λ1 1 = v= vstringstring / / 2L 2L NodeNodeNodeNodeAntinodeAntinodePhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord80/2080/20The 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” ]NodeNodeNodeNodeNodeNodeAntinodeAntinodeAntinodeAntinodeλλ2 2 /4/4λλ2 2 /4/4λλ2 2 /4/4λλ2 2 /4/4L = L = 44/₄/₄ λλ22Second Second HarmonicHarmonicff22 = v = vstringstring / λ / λ2 2 = v= vstringstring / / L LPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & HarpsichordThe Vibrating String DemonstrationThe Vibrating String DemonstrationPhysics 1251Physics 1251Unit 2 Session 21Unit 2 Session 21Scales and StringsScales and Strings80/2080/20Frequency 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 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord80/2080/20The 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 modesPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & Harpsichord80/2080/20The 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, dampingPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & HarpsichordThe The GuitarGuitar is a fretted stringed is a fretted stringed instrumentinstrumentthat is plucked or strummed.that is plucked or strummed.NeckNeckBodyBodyStrings (6) Strings (6) Tuning pegsTuning pegsBridgeBridgeFretsFretsPhysics 1251Physics 1251Unit 2 Session 22Unit 2 Session 22Strings: Guitar, Harp, Piano & HarpsichordStrings: Guitar, Harp, Piano & HarpsichordDensity of strings sets range of each Density of strings sets range of each


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