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

2. Physics 1251Unit 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 1251Unit 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: f 1 = [1/(2L)] ‧ √(T/ μ)] 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: f 1 = [1/(2L)] ‧ √(T/ μ)] Standing waves on the string are responsible for the harmonic series of stringed instruments. 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. The details of the harmonic recipe depends upon the excitation of the various harmonics.

4. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A musical instrument comprises four important components: ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ (1) a mechanical energy source; (2) a frequency generator; (3) a frequency filter; (4) an antenna.

5. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A stringed instrument uses standing waves on a string to provide the frequency generation. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ String Standing Waves

6. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord A Standing Wave results from interference of counter-reflecting waves. L = 2 /₄ λ 1 λ 1 /4 Fundamental Mode f 1 = v string / λ 1 = v string / 2L NodeNode Antinode

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

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

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

10. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 The modes that will be present are those that are excited. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Energy source can excite selected modes

11. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 The modes that will be present are those that are excited. Example: Guitar Overtones (Harmonics) Plucking, strumming, damping

12. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The Guitar is a fretted stringed instrument that is plucked or strummed. Neck Body Strings (6) Tuning pegs Bridge Frets

13. Physics 1251Unit 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 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Frets shorten the string to raise the pitch. LoLoLoLo L1L1L1L1 Fret L o / L n 11.06 21.12 31.20 41.27 51.33

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

16. Physics 1251Unit 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. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 The coupling of the string to the sound board will accentuate or attenuate various frequencies. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Sound Board and Acoustics filter harmonics

18. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord The response of the body and air cavity determine the filtering of the harmonics. Bridge Sound hole Truss rod Body Neck Guitar in cross section

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

20. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harp is a stringed instrument that is plucked. Its strings are of various lengths. Traditional Irish Harp Strings Sound Board

21. Physics 1251Unit 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 However, depressing a pedal shortens or lengthens the string length, raising (or lowering) the pitch incrementally. Strings Pedals

22. Physics 1251Unit 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 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harpsichord is a keyboard stringed instrument whose strings are plucked. Each string is used for one pitch only.

24. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harpsichord is a keyboard stringed instrument whose strings are plucked. Each string is used for one pitch only.

25. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harpsichord is a keyboard stringed instrument whose strings are plucked. Each string is used for one pitch only.

26. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harpsichord is a keyboard stringed instrument whose strings are plucked. Each string is used for one pitch only. Key Jack String Plectrum Damper Harpsichord Action

27. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harpsichord is a keyboard stringed instrument whose strings are plucked. Each string is used for one pitch only.

28. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Harpsichord is a keyboard stringed instrument whose strings are plucked. Each string is used for one pitch only. Plucked

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

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

31. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Piano is a keyboard stringed instrument whose strings are hammered. Each string is used for one pitch only. Strings Key Board SoundBoard FortepianoPiano

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

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

34. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/20 A Piano has multiple strings (in the treble) to provide a more powerful sound. Multiple Strings Sound Board BridgeFrame

35. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Piano strings are tensioned by tuning pins in a strong frame. Frame Tuning Pins Bass Strings

36. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Piano hammers are made of felt and wood. Pivot hinge Hammer Head Back Check Felt Wood

37. Physics 1251Unit 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. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord 80/ 20 The timbre of a musical instrument is determined by the excitation, frequency generation, filtering and broadcast of the harmonics. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Excitation f Generation f Generation f Response Broadcast

39. Physics 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Summary: f n = [n/(2L)] ‧ √(T/ μ) f n = [n/(2L)] ‧ √(T/ μ) The node-antinode distance is ¼ λ. The node-antinode distance is ¼ λ. The timbre of a stringed instrument is determined by its harmonic recipe. 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. 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 1251Unit 2 Session 22 Strings: Guitar, Harp, Piano & Harpsichord Summary: A Guitar is a stringed instruments with frets played by plucking. A Guitar is a stringed instruments with frets played by plucking. A Harp is a fretless stringed instrument 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 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. The Piano is a stringed instrument with a keyboard that causes a felt hammer to strike the string.