Lecture 14: Musical Instruments
Musical Instruments
Introductory Concepts
Tapped Wineglass: A tapped wineglass produces a sound with a characteristic tone that decays over time.
To break a glass with sound, take into consideration the following:
Decay Time:
Choose a glass with a long decay time and expose it to its characteristic tone.
Choose a glass with a short decay time and expose it to its characteristic tone.
Choose a glass with a long decay time and expose it to a sudden sound.
Choose a glass with a short decay time and expose it to a sudden sound.
Observations about Musical Instruments
Musical instruments have distinct characteristics:
They can produce different notes.
They must be tuned to produce the correct musical notes.
They can sound different even when playing the same note.
They require energy input to create sound.
Questions about Musical Instruments
Why do strings produce specific notes?
What gives a vibrating string its characteristic sound associated with stringed instruments?
How does bowing cause a string to vibrate?
Why do stringed instruments need surfaces?
What is vibrating in a wind instrument?
Why does a drum sound particularly different?
String Vibrations
Why do Strings Produce Specific Notes?
Properties of a Taut String:
A taut string exhibits:
A mass contributing to its inertia.
Tension providing a spring-like characteristic.
A stable equilibrium shape (straight line).
Restoring forces proportional to the string's displacement.
A taut string behaves as a harmonic oscillator:
It oscillates around its equilibrium shape with a pitch that is independent of amplitude.
Perception of Vibrations
The frequency of a string’s vibration determines the pitch of the note it plays:
High frequency corresponds to high pitch.
Low frequency corresponds to low pitch.
Examples:
Low pitch: "like a rumble."
High pitch: "like a squeak."
Notable frequency values:
Hz (low A)
Hz (A note)
Hz (high A)
The amplitude of a string’s vibration determines the volume/loudness:
Greater vibration corresponds to higher amplitude and increased volume.
Tuning of Strings
The pitch of a string depends on several factors:
Stiffness (spring-like aspect):
Determined by the tension in the string and its length.
Inertial aspect:
Determined by the string's mass.
Fundamental Vibration
A string's fundamental vibrational mode features:
A displacement node at each end and an antinode at its center.
The frequency of the fundamental mode is:
Proportional to the square root of tension:
More tension equals a higher pitch.
Tuning pegs alter tension in guitar strings.
Proportional to the inverse square root of length:
Longer strings produce a lower pitch.
Placement of a finger along the fretboard alters the effective length and alters the note.
Proportional to the inverse square root of mass:
Heavier, thicker strings produce lower pitch notes.
Example on guitar:
Thinnest string (1st or E string) generates the highest notes.
Thickest string (6th string, also E) generates the lowest notes.
Harmonics and Overtones
A string can vibrate in different modes:
First overtone (2nd harmonic): has twice the fundamental pitch and two antinodes with a node in the middle.
Second overtone (3rd harmonic): has frequencies three times the fundamental pitch and three antinodes with two nodes.
The first overtone (octave) represents a doubling of frequency.
Overtones with pitches that are integer multiples of the fundamental are termed harmonics.
Bowing or plucking a string stimulates a combination of fundamental and harmonic vibrations:
The fundamental usually dominates.
The mix of frequencies contributes to the character or timbre of the sound.
Different instruments can play the same notes, yet possess unique timbres (e.g., violins vs. guitars).
Bowing Mechanism
How Bowing Causes Vibration
Resonant Energy Transfer:
Example analogy:
A woman pushing a child on a swing acts like a pendulum.
She pushes at the natural frequency of the swing to increase amplitude gradually.
This process is called resonant energy transfer or resonance:
The woman pushes the child once per swing cycle.
Each push adds energy, increasing the swing amplitude over time.
Plucking vs. Bowing:
Plucking transfers energy immediately.
Bowing transfers energy gradually, allowing energy build-up over cycles.
Example:
Tacoma Narrows Bridge collapse where wind acted like a bow on the bridge, causing resonant frequency oscillations leading to the bridge's structural failure.
Sympathetic Vibration:
This occurs when one vibrating object causes another nearby object to vibrate at its resonance frequency, transferring energy through mechanical connection (e.g., sound waves).
Soundboards and Resonance in Stringed Instruments
Purpose of Soundboards:
Strings themselves displace very little air, thus producing a faint sound.
Stringed instruments require a large surface, like a soundboard (e.g., the body of a guitar or violin), to effectively project sound.
The soundboard acts as a resonator.
Mechanism of Amplification:
Vibrations from the strings are transferred to the bridge and then to the soundboard.
The larger surface area of the soundboard vibrates a significantly greater volume of air.
This efficient transfer of energy to the air amplifies the sound produced by the instrument.
The shape, material, and construction of the soundboard greatly influence the instrument's timbre and volume.
Wind Instruments
Vibrating Element:
In wind instruments, the vibrating element that produces sound is an air column.
The player's breath causes the air column within the instrument to resonate.
Pitch Generation:
The pitch of the note produced is primarily determined by the effective length of the air column.
Longer air columns produce lower pitches.
Shorter air columns produce higher pitches.
Instruments achieve different effective lengths through:
Finger holes (e.g., flute, clarinet, saxophone): Opening and closing holes changes the point at which the air column effectively ends.
Slides (e.g., trombone): A movable slide alters the physical length of the tube.
Valves (e.g., trumpet, tuba): Pressing valves opens up additional tubing sections, effectively lengthening the air column.
Sound Production Types:
Brass Instruments: Sound is produced by the player's lips vibrating against the mouthpiece, creating a buzz that excites the air column.
Woodwind Instruments: Sound is produced by:
Reeds (single or double): Air blown across a reed causes it to vibrate (e.g., clarinet, saxophone, oboe, bassoon).
Air across an edge: Air is directed across an edge or hole, causing the air column to resonate (e.g., flute, recorder, piccolo).
Percussion Instruments
Distinct Sound Characteristics:
Percussion instruments produce sound through striking, scraping, or shaking, causing a membrane, bar, or object to vibrate.
They often produce sounds with a more complex harmonic structure compared to strings or wind instruments, contributing to their unique timbre.
Drums:
Vibrating Element: The primary sound source is a stretched membrane (drumhead) or the entire body of the instrument.
Pitch and Timbre Factors:
Size of the drumhead: Larger drumheads generally produce lower pitches.
Tension of the drumhead: Tighter membranes produce higher pitches.
Material of the drumhead and shell: Affects the resonance and overtone characteristics.
Striking location: Hitting the center or edge can change the mix of overtones and the resulting sound.
Indefinite vs. Definite Pitch:
Many drums (e.g., snare drum, bass drum, tom-toms) produce indefinite pitch, meaning their vibrations create a complex set of frequencies that don't correspond to a clear musical note.
Some drums (e.g., timpani, tabla) can produce definite pitch because their design allows for controllable overtone tuning, making them capable of playing specific notes.