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Musical Instruments 1 Musical Instruments. Musical Instruments 2 Introductory Question Sound can break glass. Which is most likely to break: Sound can.

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Presentation on theme: "Musical Instruments 1 Musical Instruments. Musical Instruments 2 Introductory Question Sound can break glass. Which is most likely to break: Sound can."— Presentation transcript:

1 Musical Instruments 1 Musical Instruments

2 Musical Instruments 2 Introductory Question Sound can break glass. Which is most likely to break: Sound can break glass. Which is most likely to break: A. A glass pane exposed to a loud, short sound B. A glass pane exposed to a certain loud tone C. A crystal glass exposed to a loud, short sound D. A crystal glass exposed to a certain loud tone

3 Musical Instruments 3 Observations about Musical Instruments They can produce different notes They can produce different notes They must be tuned to produce the right notes They must be tuned to produce the right notes They sound different, even on the same note They sound different, even on the same note They require power to create sound They require power to create sound

4 Musical Instruments 4 4 Questions about Musical Instruments Why do strings produce specific notes? Why do strings produce specific notes? Why does a vibrating string sound like a string? Why does a vibrating string sound like a string? Why do stringed instruments need surfaces? Why do stringed instruments need surfaces? What is vibrating in a wind instrument? What is vibrating in a wind instrument?

5 Musical Instruments 5 Question 1 Why do strings produce specific notes? Why do strings produce specific notes?

6 Musical Instruments 6 Oscillations of a Taut String A taut string has A taut string has a mass that provides it with inertia a mass that provides it with inertia a tension that provides restoring forces a tension that provides restoring forces a stable equilibrium shape (straight line) a stable equilibrium shape (straight line) restoring forces proportional to displacement restoring forces proportional to displacement A taut string is a harmonic oscillator A taut string is a harmonic oscillator It oscillates about its equilibrium shape It oscillates about its equilibrium shape Its pitch is independent of its amplitude (volume)! Its pitch is independent of its amplitude (volume)!

7 Musical Instruments 7 A Taut String’s Pitch Stiffness of a string’s restoring forces are set by Stiffness of a string’s restoring forces are set by the string’s tension the string’s tension the string’s curvature (or, equivalently, length) the string’s curvature (or, equivalently, length) The inertial characteristics of a string are set by The inertial characteristics of a string are set by the string’s mass per length the string’s mass per length

8 Musical Instruments 8 Fundamental Vibration A string has a fundamental vibrational mode A string has a fundamental vibrational mode in which it vibrates as a single arc, up and down, in which it vibrates as a single arc, up and down, with a velocity antinode at its center with a velocity antinode at its center and velocity nodes at its two ends and velocity nodes at its two ends Its fundamental pitch (frequency of vibration) is Its fundamental pitch (frequency of vibration) is proportional to its tension, proportional to its tension, inversely proportional to its length, inversely proportional to its length, and inversely proportional to its mass per length and inversely proportional to its mass per length

9 Musical Instruments 9 Question 2 Why does a vibrating string sound like a string? Why does a vibrating string sound like a string?

10 Musical Instruments 10 Overtone Vibrations A string can also vibrate as A string can also vibrate as two half-strings (one extra antinode) two half-strings (one extra antinode) three third-strings (two extra antinodes) three third-strings (two extra antinodes) etc. etc. These higher-order vibrational modes These higher-order vibrational modes have higher pitches than the fundamental mode have higher pitches than the fundamental mode and are called “overtones” and are called “overtones”

11 Musical Instruments 11 A String’s Harmonics (Part 1) A string’s overtones are special: harmonics A string’s overtones are special: harmonics First overtone involves two half-strings First overtone involves two half-strings Twice the fundamental pitch: 2 nd harmonic Twice the fundamental pitch: 2 nd harmonic One octave above the fundamental frequency One octave above the fundamental frequency Second overtone involves three third-strings Second overtone involves three third-strings Three times the fundamental pitch: 3 rd harmonic Three times the fundamental pitch: 3 rd harmonic An octave and a fifth above the fundamental An octave and a fifth above the fundamental Etc. Etc.

12 Musical Instruments 12 A String’s Harmonics (Part 2) Integer overtones are called “harmonics” Integer overtones are called “harmonics” Bowing or plucking a string excites a mixture of fundamental and harmonic vibrations, giving the string its characteristic sound Bowing or plucking a string excites a mixture of fundamental and harmonic vibrations, giving the string its characteristic sound

13 Musical Instruments 13 Question 3 Why do stringed instruments need surfaces? Why do stringed instruments need surfaces?

14 Musical Instruments 14 Projecting Sound In air, sound consists of density fluctuations In air, sound consists of density fluctuations Air has a stable equilibrium: uniform density Air has a stable equilibrium: uniform density Disturbances from uniform density make air vibrate Disturbances from uniform density make air vibrate Vibrating strings barely project sound because Vibrating strings barely project sound because air flows around thin vibrating objects air flows around thin vibrating objects and is only slightly compressed or rarefied and is only slightly compressed or rarefied Surfaces project sound much better because Surfaces project sound much better because air can’t flow around surfaces easily air can’t flow around surfaces easily and is substantially compressed or rarefied and is substantially compressed or rarefied

15 Musical Instruments 15 Plucking and Bowing Plucking a string transfers energy instantly Plucking a string transfers energy instantly Bowing a string transfers energy gradually Bowing a string transfers energy gradually Bow does a little work on the string every cycle Bow does a little work on the string every cycle Excess energy builds up gradually in the string Excess energy builds up gradually in the string This gradual buildup is resonant energy transfer This gradual buildup is resonant energy transfer The string will vibrate sympathetically when The string will vibrate sympathetically when another object vibrates at its resonant frequency another object vibrates at its resonant frequency and it gradually obtains energy from that object and it gradually obtains energy from that object

16 Musical Instruments 16 Introductory Question (revisited) Sound can break glass. Which is most likely to break: Sound can break glass. Which is most likely to break: A. A glass pane exposed to a loud, short sound B. A glass pane exposed to a certain loud tone C. A crystal glass exposed to a loud, short sound D. A crystal glass exposed to a certain loud tone

17 Musical Instruments 17 Question 4 What is vibrating in a wind instrument? What is vibrating in a wind instrument?

18 Musical Instruments 18 Oscillations of Air in a Tube Air in a tube has Air in a tube has a mass that provides it with inertia a mass that provides it with inertia a pressure distribution that provides restoring forces a pressure distribution that provides restoring forces a stable equilibrium structure (uniform density) a stable equilibrium structure (uniform density) restoring forces proportional to displacement restoring forces proportional to displacement Air in a tube is a harmonic oscillator Air in a tube is a harmonic oscillator It oscillates about its equilibrium density distribution It oscillates about its equilibrium density distribution Its pitch is independent of its amplitude (volume)! Its pitch is independent of its amplitude (volume)!

19 Musical Instruments 19 Air in a Tube’s Pitch Stiffness of the air’s restoring forces are set by Stiffness of the air’s restoring forces are set by the air’s pressure the air’s pressure the air’s pressure gradient (or, equivalently, length) the air’s pressure gradient (or, equivalently, length) The inertial characteristics of the air are set by The inertial characteristics of the air are set by the air’s mass per length the air’s mass per length

20 Musical Instruments 20 Fundamental Vibration Open-Open Column Air column vibrates as a single object Air column vibrates as a single object Pressure antinode occurs at column center Pressure antinode occurs at column center Pressure nodes occur at column ends Pressure nodes occur at column ends Pitch (frequency of vibration) is Pitch (frequency of vibration) is proportional to air pressure proportional to air pressure inversely proportional to column length inversely proportional to column length inversely proportional to air density inversely proportional to air density

21 Musical Instruments 21 Fundamental Vibration Open-Closed Column Air column vibrates as a single object Air column vibrates as a single object Pressure antinode occurs at closed end Pressure antinode occurs at closed end Pressure node occurs at open end Pressure node occurs at open end Air column in open-closed pipe vibrates Air column in open-closed pipe vibrates as half the column in an open-open pipe as half the column in an open-open pipe at half the frequency of an open-open pipe at half the frequency of an open-open pipe

22 Musical Instruments 22 Air Harmonics (Part 1) In open-open pipe, the overtones are at In open-open pipe, the overtones are at twice fundamental (two pressure antinodes) twice fundamental (two pressure antinodes) three times fundamental (three antinodes) three times fundamental (three antinodes) etc. (all integer multiples or “harmonics”) etc. (all integer multiples or “harmonics”) In open-closed pipe, the overtones are at In open-closed pipe, the overtones are at three times fundamental (two antinodes) three times fundamental (two antinodes) five times fundamental (three antinodes) five times fundamental (three antinodes) etc. (all odd integer multiples or “harmonics”) etc. (all odd integer multiples or “harmonics”)

23 Musical Instruments 23 Air Harmonics (Part 2) Blowing across the column tends to excite a mixture of fundamental and harmonic vibrations Blowing across the column tends to excite a mixture of fundamental and harmonic vibrations Examples Examples Organ pipes Organ pipes Recorders Recorders Flutes Flutes Whistles Whistles Reeds and horns also use a vibrating air column Reeds and horns also use a vibrating air column

24 Musical Instruments 24 Surface Instruments Most 1-dimensional instruments Most 1-dimensional instruments can vibrate at half, third, quarter length, etc. can vibrate at half, third, quarter length, etc. harmonic oscillators with harmonic overtones harmonic oscillators with harmonic overtones Most 2- or 3- dimensional instruments Most 2- or 3- dimensional instruments have complicated higher-order vibrations have complicated higher-order vibrations harmonic oscillators with non-harmonic overtones harmonic oscillators with non-harmonic overtones Examples: drums, cymbals, bells Examples: drums, cymbals, bells

25 Musical Instruments 25 Drumhead Vibrations

26 Musical Instruments 26 Summary of Musical Instrument use strings, air, etc. as harmonic oscillators use strings, air, etc. as harmonic oscillators pitches independent of amplitude/volume pitches independent of amplitude/volume tuned by tension/pressure, length, density tuned by tension/pressure, length, density often have harmonic overtones often have harmonic overtones project vibrations into the air as sound project vibrations into the air as sound


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