9.2 Musical Instruments. New Ideas for today Sound and waves Pitch String and wind instruments.
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Transcript of 9.2 Musical Instruments. New Ideas for today Sound and waves Pitch String and wind instruments.
Sound is a wave!Sound is a wave!Sound is a wave!Sound is a wave!
• Sound is a longitudinal pressure wave in a medium (gas, liquid or solid)
• Anything that vibrates a medium produces sound
• Air is the most common medium for carrying sound
• Sound is a longitudinal pressure wave in a medium (gas, liquid or solid)
• Anything that vibrates a medium produces sound
• Air is the most common medium for carrying sound
Bell in vacuumBell in vacuum
•Waves have a wavelength: distance to next crest or trough
•Waves have an amplitude: peak change in pressure for sound in air
•Any mechanical wave “represents the natural motion of an extended object around stable equilibrium shape or situation”
Watch one place – the period is the time for the next crest or trough to appear
Watch one crest – moves at the speed of sound (330 m/s in air)
The frequency, or pitch, of sound is the number of times per second that the wave repeats itself (or 1/period)
wave speed = frequency × wavelength
http://phet.colorado.edu/simulations/sound/sound.jnlp
PitchPitch
Western musical scale constructed around A4, or 440 Hz. Crests repeat 440 times per second at one point in space!
IntervalsIntervalsIntervalsIntervals
Playing two frequencies together sounds nice when they are in small integer ratios
• Octave 2:1• Fifth 3:2• Fourth 4:3• Third 5:4
Playing two frequencies together sounds nice when they are in small integer ratios
• Octave 2:1• Fifth 3:2• Fourth 4:3• Third 5:4
KeyboardKeyboard
Equal temperamentEqual temperament
•Notice anything funny?
G4 / C4=1.498…
•Most Western music written around half-steps
Ratio between adjacent frequencies = 12 2 1.05946...
•Makes every key sound similar (every key equally mistuned)
•Orchestras will sometimes tune specially for particular pieces
An object’s natural vibration or resonant frequency is determined by its: Mass Size and shape Elastic nature (stiffness) Composition
Musical resonators Stretched strings (violin string) Hollow tubes (flute) Stretched membrane (drum)
An object’s natural vibration or resonant frequency is determined by its: Mass Size and shape Elastic nature (stiffness) Composition
Musical resonators Stretched strings (violin string) Hollow tubes (flute) Stretched membrane (drum)
Tacoma Narrows Bridge – a wind instrument!
Producing Musical SoundProducing Musical SoundUsually involves a resonator
String as Harmonic String as Harmonic OscillatorOscillatorString as Harmonic String as Harmonic OscillatorOscillator Its mass gives it inertia Its tension and curvature give it a restoring force It has a stable equilibrium Its restoring force is proportional to displacement
Its mass gives it inertia Its tension and curvature give it a restoring force It has a stable equilibrium Its restoring force is proportional to displacement
Clicker questionClicker questionWhy does the low E string have copper wrapped around it?
A. To increase the tension of the string.B. To increase the mass of the string.C. To change the length of the string.D. To increase the thermal conductivity of the string.
Modes of OscillationModes of OscillationModes of OscillationModes of OscillationFundamental Vibration (First Harmonic)
Center of string vibrates up and down Frequency of vibration (pitch) is
proportional to tension inversely proportional to length inversely proportional to density (mass/length)
Fundamental Vibration (First Harmonic) Center of string vibrates up and down Frequency of vibration (pitch) is
proportional to tension inversely proportional to length inversely proportional to density (mass/length)
Stringed instrumentStringed instrument
Wine glassWine glass
Wine glass IIWine glass II
Modes of OscillationModes of OscillationModes of OscillationModes of Oscillation Higher-Order Vibrations (Overtones or Harmonics)
Second harmonic is like two half-strings Third harmonic is like three third-strings, …
Each higher mode has one more node in its oscillation Harmonics come in integer multiples (1,2,3,4…)
Higher-Order Vibrations (Overtones or Harmonics) Second harmonic is like two half-strings Third harmonic is like three third-strings, …
Each higher mode has one more node in its oscillation Harmonics come in integer multiples (1,2,3,4…)
Fundamental
2nd Harmonic 3rd Harmonic 4th Harmonic
Wavelength =
Transverse Standing Waves
Standing waveStanding wave
TimbreTimbre
Frequency (Hz)
Volu
me
Instruments have different musical fingerprint, or spectra
Frequency analyzerFrequency analyzer
The Sound BoxThe Sound BoxThe Sound BoxThe Sound Box Strings don’t project sound well
Air flows around objects Surfaces project sound much better
Air can’t flow around surfaces easily Movement of air is substantial!
Strings don’t project sound well Air flows around objects
Surfaces project sound much better Air can’t flow around surfaces easily Movement of air is substantial!
GuitarsGuitars
SpeakerSpeaker
Beautiful MusicBeautiful MusicBeautiful MusicBeautiful Music Transfer of vibration to a “sound box” is important in
instrument design helps to project the sound effectively helps to “color” the sound, making the instrument sound
unique The method of exciting the string also affects the sound.
Plucking a string transfers energy quickly and excites many vibrational modes
Bowing a string transfers energy slowly excites the string at its fundamental frequency each stroke adds to the string’s vibrational energy
Transfer of vibration to a “sound box” is important in instrument design helps to project the sound effectively helps to “color” the sound, making the instrument sound
unique The method of exciting the string also affects the sound.
Plucking a string transfers energy quickly and excites many vibrational modes
Bowing a string transfers energy slowly excites the string at its fundamental frequency each stroke adds to the string’s vibrational energy
Air Column as Resonant Air Column as Resonant SystemSystemAir Column as Resonant Air Column as Resonant SystemSystem
f0
2f0
3f0
A column of air is a harmonic oscillator Its mass gives it inertia Pressure gives it a restoring force It has a stable equilibrium Restoring forces are proportional
to displacement Stiffness of restoring forces
determined by pressure pressure gradient
A column of air is a harmonic oscillator Its mass gives it inertia Pressure gives it a restoring force It has a stable equilibrium Restoring forces are proportional
to displacement Stiffness of restoring forces
determined by pressure pressure gradient
Air Column PropertiesAir Column PropertiesAir Column PropertiesAir Column Properties An air column vibrates as a single object
Pressure antinode occurs at center of open column Velocity antinode occurs at ends of open column
Pitch (frequency) is inversely proportional to column length inversely proportional to air density
An air column vibrates as a single object Pressure antinode occurs at center of open column Velocity antinode occurs at ends of open column
Pitch (frequency) is inversely proportional to column length inversely proportional to air density
Length
Length
Line of fireLine of fire
Organ pipeOrgan pipe
Singing tubesSinging tubes
BottleBottle
Air Column PropertiesAir Column PropertiesAir Column PropertiesAir Column Properties Just like a string, an air column can vibrate at
many different frequencies. A closed pipe vibrates as half an open pipe
pressure antinode occurs at sealed end frequency is half that of an open pipe
Just like a string, an air column can vibrate at many different frequencies.
A closed pipe vibrates as half an open pipe pressure antinode occurs at sealed end frequency is half that of an open pipe
Open Column Closed Column