Fundamentals of Sound |
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Fundamentals of Sound: definitions and scope of study |
Sound, Music, Noise: essential and operational definitions |
Basic Physical Variables and Units - Review |
Fundamentals of Sound: definitions and scope of study
DEFINITIONS
The study of sound is a multidisciplinary field that deals with the physical (e.g. vibrations, waves), physiological (e.g. construction of the ear), and perceptual (e.g. auditory sensations) correlates of sound production, transmission, processing, storing, reproduction, and reception. It forges a link among the physical, physiological, and perceptual frames of reference, examining ways in which physical and physiological aspects interact to gives rise to auditory sensations/perceptions.
An extension of this general study of sound, Cognitive Psychology of Sound addresses implicit and explicit processes involved in the organization of sonic perceptions into meaningful wholes and provides empirical support to the understanding of how we interpret and evaluate sound and sound structures. Cognitive Psychology of Sound is addressed in more detail elsewhere and will only be addressed here in passing.
For a good, comprehensive, introductory resource see Music & Science (at the Center for Music & Science; University of Cambridge)"Frame of reference": A collection of concepts/definitions accepted by a particular field or bounded area of discourse, representing a particular world view.
In our study of sound will delve into several of the Acoustics Fields:
Physical Acoustics (vibrational/physical frame of reference): examination of sound in terms of generation, transmission and modification of acoustic waves.
How is sound produced and how is it influenced by sound source material, construction, and excitation?
How does sound wave transmission through the air, etc. modify the sound before it reaches our ears?
What are the physical bases of our meaningful and emotional responses to sound?
Out of the many relevant areas, we will be touching on Musical, Architectural, and Environmental Acoustics.Physiological Acoustics (biological/physiological frame of reference): human body reaction to sound vibrations.
How and with what accuracy do our ears process acoustic energy and how do they transform it into auditory sensations?
What are the physiological bases of our meaningful and emotional responses to sound?
The combination of Physical and Physiological Acoustics outlines the discipline of Psychoacoustics.Signal processing / Notation (symbolic frame of reference): examination of sound waves in terms of their electronic, graphic, and mathematical representations; a special case of semiotics, to which music notation also belongs.
How does manipulating analogues/symbols relate to manipulating acoustic waves and sound sensations, and vice versa?
What is the formal basis of our meaningful and emotional responses to sound?
In the context of our course, we will be limiting our investigation to a small subset of graphic representations of sound (i.e. sound signals & spectra) and to the conceptual understanding of digital audio basics.
In our study of sound we will identify
sensation limits or absolute thresholds:
absolute lowest/highest magnitudes (levels) of a vibration/wave that safely and reliably give rise to a corresponding sonic sensation
relative sensation thresholds or difference thresholds or Just Noticeable Differences (JNDs):
minimum amount of change in a physical variable, necessary to elicit a perceived change in sonic sensation
type of relationship between physical and perceived changes
(e.g. direct versus inverse relationship; linear versus nonlinear relationship; type of nonlinearity)
changes in 1-3 due to a vibration's/wave's duration and level
(e.g. issues of adaptation, fatigue, etc., related to the length and intensity of exposure to sonic stimuli)
changes in 1-4 due to context and stimulus interactions
(e.g. due to the simultaneous, past, or future presence of additional stimuli, whether sonic or otherwise)
Sound, Noise, Music: essential and operational definitions
Essential definition: a definition of a concept that
(a) includes components that are both necessary (i.e. without them the concept would lose its identity) and sufficient (i.e. no other components are needed) to the concept's description, within a given context
and
(b) uniquely identifies it (i.e. no other concept shares exactly the same defining components, within a given context).
Operational definition: an essential definition of a concept that also outlines possible operations (i.e. processes; numerical or otherwise) that assist in the reliable identification and measurement of the concept's occurrences, within a given context.
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SOUND
The term "sound" is often used loosely to refer to
several
phenomena/observations: Review the 3 video examples of sonic energy visualization. |
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NOISE The term "noise" is
also used differently, depending on
frame of reference (physics vs. communication) and context. |
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Noise as "Unwanted Sound" |
Noise Music |
In our course, we will be alternating between the two definitions, below, depending on ... context. |
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Noise is: |
Noise is: |
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"How Music Works" - David Byrne (2012) seven short video interviews on the book with the same name (book review by The Guardian) |
MUSIC For the purposes
of this course, we adopt the following operational definition: The importance of context is a direct consequence of music as communication. All communication involves shared and unshared knowing, and this is what we will broadly refer to as context. Analogously to abstract animation, the potential of music to communicate a-referentially, that is without necessarily having to refer/point to anything other the sounds themselves, distinguishes it from linguistic communication. Music may be seen as a "noun-less" language, made just from verbs (potential / motion / action / narrative; concepts with a fundamentally temporal dimension). |
MUSIC & COMMUNICATION
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THE WORLD OF MUSIC |
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Excerpt from 'Raga Hameer'. Traditional piece arranged
by Vilayat Khan. 'The Music of India and Pakistan' CD. The Rough
Guide. World Music Network © 1995. Titles from the film "Forbidden Planet" (1956). 'Electronic tonalities' by Luis and Bebe Baron. Music from the trailer for "Forbidden Planet". The unconventional music of the film has been replaced by a conventional, trendy (for its time) score, in the hopes of reaching a wider audience. The music is filled with referential aspects [musical passages that simply act as "pointers"] trading on the success of other contemporary films (e.g. Ben Hur) and on the popularity of widely accepted musical associations (e.g. lyrical strings and florid flute passages during the "woman in water" scene). Titles from the film "The Day The Earth Stood Still" (1951). First film score in stereo; first popular film using a Theremin; score by Bernard Hermann. First monolith scene from the film "2001: A Space Odyssey" (1968). 'Requiem' by G.Ligeti. Opening scene from the film "The Matrix" (1999). Full version; score by Don Davis. Opening scene from the film "The Matrix" (1999). Score only. |
Basic physical variables and units - Review
Math Symbols & Units - (source)
Acoustics is based on the following three fundamental concepts/measures/units. All other acoustical concepts/measures/units derive from these three:
Mass (kg: kilogram)
Length/Distance (m: meter)
Time (s: second)
According to the International System of Units (SI), there is a total of 7 base units. The above three plus: iv) electric current (A: ampere); v) thermodynamic temperature (K: kelvin); vi) amount of substance (mol: mole); and vii) luminous intensity (cd: candela)Velocity: v = ds/dt (change in distance per unit time) - Unit: m/s (meters per second).
Velocity of 1 m/s represents an increase in distance (away from a reference point) by 1 meter, each second.Acceleration: a = dv/dt (change in velocity per unit time) - Unit: m/s2 (meters per second-squared).
Acceleration of 1 m/s2 represents an increase in velocity by 1 m/s, each second.Force: F = m*a (mass times acceleration). In terms of gravity, a = g = 9.81 m/s2 and F = m*g - Unit: 1 Newton (N). 1 N = 1 Kg*m/s2.
Force of 1 N represents the force that must be applied to a mass of 1 Kg in order to accelerate it by 1 m/s2.
Newton’s Laws of motion: a) If F = 0, v is constant b) F = m*a c) Action – ReactionPressure: P = F/A (force per unit area) - Unit: 1 Pascal (Pa). 1 Pa = 1 N/m2. = 1 Kg/(m*s2).
Pressure of 1 Pa represents a force of 1 Newton applied over an area of 1 square meter.
Atmospheric pressure (at sea level): Patm = 105 N/m2.
Smallest pressure fluctuation that can be perceived as sound (limit threshold for pressure fluctuation) : Pref = 2*10-5 N/m2.Work/Energy: E = F*ds (work done by a force F when it moves a mass m over a distance ds) - Unit: 1 Joule (J). 1 J = 1 N*m.
If the mass is lifted at a height h, its potential energy (manifested as load) is: Ep = F*h = m*g*h.
If the mass is in motion with speed v, its kinetic energy (manifested as motion) is Ek = (1/2)m*v2.
1 J is the energy needed to move a mass of 1 Kg for 1 meter.
Types of energy: Mechanical, electrical, thermal, chemical, etc.Examples:
Potential energy for a spring with spring constant K (measure of a spring's stiffness) displaced from rest by a distance y --> Ep = (1/2)K*y2
Take-away: The energy stored in a spring is proportional to its stiffness and to the square of its compression/expansion away from rest.
Potential energy for a string with tension T and length L, displaced from rest by a distance y --> Ep = 2T*y2/L
Take-away: Analogously to a spring, the energy stored in a string is proportional to its stiffness and to the square of its displacement away from rest but it is inversely proportional to its lengthPower: W = E/t (amount of energy production/consumption/transfer per unit time) - Unit: 1 Watt (W). 1 W = 1 J/sec.
Power of 1 W means that energy of 1 J is produced/consumed/transferred within a system every second.In terms of hearing
a) Pressure is a more meaningful measure than Force and
b) Power is a more meaningful measure to hearing than Energy.
Why? The answer can be inferred further below.
Intensity combines in a single measure the advantages (with regards to hearing) of Pressure over Force and of Power over Energy.]Intensity: I = W/A (power per unit area) - Unit: 1 W/m2.
Intensity of 1W/m2 represents the production/consumption/transfer of 1 J of energy, through an area of 1 m2, each second.As an expression of the amount of energy in a vibrational system, Intensity is more meaningful and useful that Energy or Power because it allows for energy comparisons irrespective of a vibration’s duration or the spatial spread of the resulting wave. This matches the perceptual salience of rates of change over a given area rather than of absolute quantities, salience that is related to the auditory system's construction and function.
Smallest vibration intensity that can be perceived as sound: Iref = 10-12 W/m2.
In vibrations, Energy, Power and, consequently, Intensity are all proportional to the square of both frequency and amplitude.
(Optional: Can you infer this from the expression for Kinetic Energy?).
For waves in gases/liquids, intensity I is also proportional to the square of pressure: I = kP2 (where k is a constant).
(Optional: note that pressure P is proportional to the square root of the gas's density ρ and of the speed of wave propagation c [i.e. P= (Iρc)0.5]).
Loyola Marymount University - School of Film & Television