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Physics 1251 The Science and Technology of Musical Sound

Physics 1251 The Science and Technology of Musical Sound. Unit 2 Session 22 MWF Strings: Guitar, Harp, Piano and Harpsichord. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord. Foolscap Quiz:

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Physics 1251 The Science and Technology of Musical Sound

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  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) √(T/ μ) f = 1/(2‧1.02) √(800/0.006) f = 179.0 Hz

  3. 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)] ‧ √(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.

  4. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ 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.

  5. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ 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

  6. L = 2/₄ λ1 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 / λ1 = vstring / 2L Node Node Antinode λ1 /4 λ1 /4

  7. L = 4/₄ λ2 Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20The distance between neighboring nodes & antinodes is ¼ λ. [ “N-A d = ¼ λ” ] Second Harmonic f2 = vstring / λ2 = vstring / L Node Node Node Antinode Antinode λ2 /4 λ2 /4 λ2 /4 λ2 /4

  8. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The Vibrating String Demonstration

  9. Physics 1251 Unit 2 Session 21 Scales and Strings 80/20Frequency of nth harmonic: fn = [2n/(4L)] ‧ vstring fn = [n/(2L)] ‧ √(T/ μ)]

  10. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The tuning pegs change the string tension. Tuning Pegs

  16. 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

  17. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ 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

  18. 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

  19. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Vibration Modes of Guitar Body: Holographic vibration images of Guitar body

  20. 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

  21. 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.

  22. 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.

  23. 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.

  24. 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

  29. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The jack plucks in one direction, then retracts in the opposite.

  30. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord A Hammer Dulcimer or Cibolo

  31. 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

  32. String and Damper Hammer Jack Key Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The Piano strings are hammered by a felt hammer, actuated by the “action.”

  33. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The Piano strings are hammered by a felt hammer, actuated by the “action.”

  34. 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

  35. 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

  36. 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

  37. 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?

  38. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ 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

  39. Physics 1251 Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Summary: • fn = [n/(2L)] ‧ √(T/ μ) • The node-antinode distance is ¼ λ. • 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.

  40. 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.

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