musical instruments 1 musical instruments. musical instruments 2 introductory question sound can...

Musical Instruments 1

Musical Musical InstrumentsInstruments


Introductory QuestionIntroductory Question

Sound can break glass. Which is most likely Sound can break glass. Which is most likely to break:to break:

A.A. A glass pane exposed to a loud, short soundA glass pane exposed to a loud, short sound

B.B. A glass pane exposed to a certain loud toneA glass pane exposed to a certain loud tone

C.C. A crystal glass exposed to a loud, short A crystal glass exposed to a loud, short soundsound

D.D. A crystal glass exposed to a certain loud A crystal glass exposed to a certain loud tonetone


Observations about Observations about Musical InstrumentsMusical Instruments

They can produce different notesThey can produce different notes They must be tuned to produce the They must be tuned to produce the

right notesright notes They sound different, even on the They sound different, even on the

same notesame note They require power to create soundThey require power to create sound


4 Questions about4 Questions aboutMusical InstrumentsMusical Instruments

Why do strings produce specific Why do strings produce specific notes?notes?

Why does a vibrating string sound Why does a vibrating string sound like a string?like a string?

Why do stringed instruments need Why do stringed instruments need surfaces?surfaces?

What is vibrating in a wind What is vibrating in a wind instrument?instrument?


Question 1Question 1

Why do strings produce specific Why do strings produce specific notes?notes?


Oscillations of a Taut Oscillations of a Taut StringString

A taut string hasA taut string has a mass that provides it with inertiaa mass that provides it with inertia a tension that provides restoring forcesa tension that provides restoring forces a stable equilibrium shape (straight line)a stable equilibrium shape (straight line) restoring forces proportional to restoring forces proportional to

displacementdisplacement A taut string is a harmonic oscillatorA taut string is a harmonic oscillator

It oscillates about its equilibrium shapeIt oscillates about its equilibrium shape Its pitch is independent of its amplitude Its pitch is independent of its amplitude

(volume)!(volume)!


A Taut String’s PitchA Taut String’s Pitch

Stiffness of a string’s restoring Stiffness of a string’s restoring forces are set byforces are set by the string’s tensionthe string’s tension the string’s curvature (or, equivalently, the string’s curvature (or, equivalently,

length)length) The inertial characteristics of a The inertial characteristics of a

string are set bystring are set by the string’s mass per lengththe string’s mass per length


Fundamental VibrationFundamental Vibration

A string has a fundamental vibrational modeA 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 centerwith a velocity antinode at its center and velocity nodes at its two endsand velocity nodes at its two ends

Its fundamental pitch (frequency of vibration) Its fundamental pitch (frequency of vibration) isis 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 lengthand inversely proportional to its mass per length



Why does a vibrating string sound Why does a vibrating string sound like a string?like a string?


Overtone VibrationsOvertone Vibrations

A string can also vibrate asA 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 These higher-order vibrational modesmodes have higher pitches than the have higher pitches than the

fundamental modefundamental mode and are called “overtones”and are called “overtones”


A String’s Harmonics A String’s Harmonics (Part (Part 1)1)

A string’s overtones are special: harmonicsA string’s overtones are special: harmonics First overtone involves two half-stringsFirst overtone involves two half-strings

Twice the fundamental pitch: 2Twice the fundamental pitch: 2ndnd harmonic harmonic One octave above the fundamental frequencyOne octave above the fundamental frequency

Second overtone involves three third-stringsSecond overtone involves three third-strings Three times the fundamental pitch: 3Three times the fundamental pitch: 3rdrd harmonic harmonic An octave and a fifth above the fundamentalAn octave and a fifth above the fundamental

Etc.Etc.


A String’s Harmonics A String’s Harmonics (Part (Part 2)2)

Integer overtones are called Integer overtones are called “harmonics”“harmonics”

Bowing or plucking a string excites a Bowing or plucking a string excites a mixture of fundamental and mixture of fundamental and harmonic vibrations, giving the harmonic vibrations, giving the string its characteristic soundstring its characteristic sound



Why do stringed instruments need Why do stringed instruments need surfaces?surfaces?


Projecting SoundProjecting Sound In air, sound consists of density fluctuationsIn air, sound consists of density fluctuations

Air has a stable equilibrium: uniform densityAir has a stable equilibrium: uniform density Disturbances from uniform density make air Disturbances from uniform density make air

vibratevibrate Vibrating strings barely project sound Vibrating strings barely project sound

becausebecause air flows around thin vibrating objectsair flows around thin vibrating objects and is only slightly compressed or rarefiedand is only slightly compressed or rarefied

Surfaces project sound much better becauseSurfaces project sound much better because air can’t flow around surfaces easilyair can’t flow around surfaces easily and is substantially compressed or rarefiedand is substantially compressed or rarefied


Plucking and BowingPlucking and Bowing

Plucking a string transfers energy instantlyPlucking a string transfers energy instantly Bowing a string transfers energy graduallyBowing a string transfers energy gradually

Bow does a little work on the string every cycleBow does a little work on the string every cycle Excess energy builds up gradually in the stringExcess energy builds up gradually in the string This gradual buildup is resonant energy transferThis gradual buildup is resonant energy transfer

The string will vibrate sympathetically whenThe string will vibrate sympathetically when another object vibrates at its resonant frequencyanother object vibrates at its resonant frequency and it gradually obtains energy from that objectand it gradually obtains energy from that object


Introductory Question Introductory Question (revisited)(revisited)

Sound can break glass. Which is most likely Sound can break glass. Which is most likely to break:to break:

A.A. A glass pane exposed to a loud, short soundA glass pane exposed to a loud, short sound

B.B. A glass pane exposed to a certain loud toneA glass pane exposed to a certain loud tone

C.C. A crystal glass exposed to a loud, short A crystal glass exposed to a loud, short soundsound

D.D. A crystal glass exposed to a certain loud A crystal glass exposed to a certain loud tonetone



What is vibrating in a wind What is vibrating in a wind instrument?instrument?


Oscillations of Air in a Oscillations of Air in a TubeTube

Air in a tube hasAir in a tube has a mass that provides it with inertiaa mass that provides it with inertia a pressure distribution that provides restoring a pressure distribution that provides restoring

forcesforces a stable equilibrium structure (uniform density)a stable equilibrium structure (uniform density) restoring forces proportional to displacementrestoring forces proportional to displacement

Air in a tube is a harmonic oscillatorAir in a tube is a harmonic oscillator It oscillates about its equilibrium density It oscillates about its equilibrium density

distributiondistribution Its pitch is independent of its amplitude Its pitch is independent of its amplitude

(volume)!(volume)!


Air in a Tube’s PitchAir in a Tube’s Pitch

Stiffness of the air’s restoring forces Stiffness of the air’s restoring forces are set byare set by the air’s pressurethe air’s pressure the air’s pressure gradient (or, the air’s pressure gradient (or,

equivalently, length)equivalently, length) The inertial characteristics of the air The inertial characteristics of the air

are set byare set by the air’s mass per lengththe air’s mass per length


Fundamental VibrationFundamental VibrationOpen-Open ColumnOpen-Open Column

Air column vibrates as a single Air column vibrates as a single objectobject Pressure antinode occurs at column Pressure antinode occurs at column

centercenter Pressure nodes occur at column endsPressure nodes occur at column ends

Pitch (frequency of vibration) isPitch (frequency of vibration) is proportional to air pressureproportional to air pressure inversely proportional to column lengthinversely proportional to column length inversely proportional to air densityinversely proportional to air density


Fundamental VibrationFundamental VibrationOpen-Closed ColumnOpen-Closed Column

Air column vibrates as a single Air column vibrates as a single objectobject Pressure antinode occurs at closed endPressure antinode occurs at closed end Pressure node occurs at open endPressure node occurs at open end

Air column in open-closed pipe Air column in open-closed pipe vibratesvibrates as half the column in an open-open pipeas half the column in an open-open pipe at half the frequency of an open-open at half the frequency of an open-open

pipepipe


Air Harmonics Air Harmonics (Part 1)(Part 1)

In open-open pipe, the overtones are atIn 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 atIn 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 etc. (all odd integer multiples or

“harmonics”)“harmonics”)


Air Harmonics Air Harmonics (Part 2)(Part 2)

Blowing across the column tends to Blowing across the column tends to excite a mixture of fundamental and excite a mixture of fundamental and harmonic vibrationsharmonic vibrations

ExamplesExamples Organ pipesOrgan pipes RecordersRecorders FlutesFlutes WhistlesWhistles

Reeds and horns also use a vibrating air Reeds and horns also use a vibrating air columncolumn


Surface InstrumentsSurface Instruments

Most 1-dimensional instrumentsMost 1-dimensional instruments can vibrate at half, third, quarter length, can vibrate at half, third, quarter length,

etc.etc. harmonic oscillators with harmonic harmonic oscillators with harmonic

overtonesovertones Most 2- or 3- dimensional instrumentsMost 2- or 3- dimensional instruments

have complicated higher-order vibrationshave complicated higher-order vibrations harmonic oscillators with non-harmonic harmonic oscillators with non-harmonic

overtonesovertones Examples: drums, cymbals, bellsExamples: drums, cymbals, bells


Drumhead VibrationsDrumhead Vibrations


Summary of Musical Summary of Musical InstrumentInstrument

use strings, air, etc. as harmonic use strings, air, etc. as harmonic oscillatorsoscillators

pitches independent of pitches independent of amplitude/volumeamplitude/volume

tuned by tension/pressure, length, tuned by tension/pressure, length, densitydensity

often have harmonic overtonesoften have harmonic overtones project vibrations into the air as project vibrations into the air as

soundsound

musical instruments 1 musical instruments. musical instruments 2 introductory question sound can...

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