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Introduction
Psychoacoustics is the branch of acoustics and psychophysics involving the scientific study of human sound perception and audiology; that is how humans perceive various sounds and the corresponding psychological responses.
Sound is mechanical radiant energy transmitted by longitudinal pressure waves in air and other materials; and as transverse waves in solids. Sound is the objective cause of hearing in humans and sounds that can be perceived include noise, speech and music.
Hearing is not a solely a mechanical phenomenon of sound wave propagation; rather it is also a sensory event and thus there are inherent human perceptions. The cochlea within the inner ear contains the cells responsible for perception. Mammals, including humans, have a coiled form of cochlea often called a mammalian cochlea. The outer hair cells of a mammalian cochlea provide enhanced sensitivity and frequency resolution. Nerve impulses then travel to the brain for perception.
Acoustics is the interdisciplinary science that deals with the study of mechanical waves propagating in gases (such as air), liquids, and solids including; mechanical waves include vibration, audible sound, ultrasound, and infrasound.
Psychophysics quantitatively studies the relationship between physical stimuli and the resulting sensations and perceptions. Psychophysics encompasses a general class of methods that can be applied to study a perceptual system. Modern applications rely heavily on threshold measurement, ideal observer analysis, and signal detection theory.
Psychophysicists typically design experimental stimuli that can be objectively measured; including pure tones varying in intensity, or lights varying in luminance. All the senses have been studied in the realm of psychophysics: vision, hearing, touch (including skin and enteric perception), taste, smell and the sense of time.
Psychoacoustics is the branch of psychophysics that studies hearing in response to audible stimuli. Sound waves propagating through air enter the ear and within the ear the sound is transformed into neural action potentials (nerve impulses). These nerve pulses then travel to the brain where sound perception occurs. Thus in the study of acoustics it is advantageous to take into account not just the mechanics of the environment; rather also to consider that both the ears and brain are involved in the listening experience.
Introduction (continued)
The human inner ear is signal processor that converts sound waves into neural stimuli; though sometimes differences in such sound waves are not perceptible. The ear has a non-linear response to sounds of different intensity levels.
Sound travels through air (and other mediums) in waves in three dimensions; however sound waves are often represented on two-dimensional graphs. Sound waves are generated by a sound source such as a vibrating diaphragm.
Frequency and Wavelength
Frequency, also called temporal frequency, is the number of occurrences of a repeating event per unit of time. The oscillations of sound waves are often characterized in terms of frequency; measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. The period is the duration (elapsed time) of one cycle in a repeating event, so the period is the reciprocal of the frequency.
Frequency is an essential concept used in science and engineering to study the rates of oscillatory and vibratory phenomena. For periodic waves, in cases where the wave speed is independent of frequency, a frequency, f, has an inverse relationship to the wavelength, λ.
Pitch is an auditory sensation related to frequency in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration.
Frequency is an objective, measurable scientific attribute; whereas pitch is each person's subjective perception of a sound wave (which cannot be directly measured). However, pitch is closely related to frequency, and it is almost entirely determined by frequency (not amplitude) with a high pitch corresponding to rapid oscillation and a low pitch corresponding to slow oscillation.
Sinusoidal Plane Waves
Sound waves are often simplified to a description in terms of sinusoidal plane waves, which are characterized by these generic properties:
f = v / λ
Limits of Perception
The human ear can nominally hear sounds in the frequency range of 20 Hz to 20,000 Hz. The upper limit tends to decrease with age; most adults are unable to hear above 16,000 Hz (16 kHz). The lowest frequency that has been identified as a musical tone is 12 Hz under ideal laboratory conditions. Tones between 4 and 16 Hz are perceived via the body's sense of touch; and are rarely heard.
Frequency resolution of the ear is about 3.6 Hz within the octave of 1000–2000 Hz. That is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a repetitive variation in volume of the tone. This amplitude modulation occurs with a frequency equal to the difference in frequencies of the two tones and is known as beating.
Sound Pressure and Intensity
Sound pressure is the local pressure deviation from ambient pressure caused by a sound wave. The unit of measure of sound pressure is the pascal (Pa). The total pressure, PTOT is equal to the the static pressure, PSTAT, plus the sound pressure, P:
PTOT = PSTAT + P
Human hearing is sensitive to sound pressure which is related to sound intensity.
Sound intensity is the power carried by sound waves per unit area in a direction perpendicular to the area. The units of measure of sound intensity are watts per square meter (W/m2). Mathematically, sound intensity, I, is the product of the sound pressure, P, and the corresponding particle velocity, v:
I = Pv
Tone and Timbre
A pure tone is a sound with a sinusoidal wave form. A complex tone is a combination of two or more pure tones that have a periodic pattern of repetition (unless specified otherwise). A musical tone is a steady periodic sound characterized by duration, pitch, intensity (or loudness), and timbre.
Timbre is the perceived sound quality of a musical note, sound, or tone; and is what distinguishes musical instruments from one another when playing the same musical note at the same volume. Two instruments can sound equally tuned as they play the same note; yet while playing at the same amplitude, level each instrument will still sound distinctive. Each instrument will have its own unique timbre, also called tone color.
In music, the envelope is a description of how a sound changes over time and can relate to elements such as amplitude, frequency and pitch. The frequency spectrum and envelope are the physical characteristics of sound that determine timbre.
Harmonic Series
An overtone is any frequency greater than the fundamental frequency of a sound. The fundamental frequency and the overtones together are called partials. A piano key when struck is identified with a fundamental frequency corresponding to the intended musical note; however overtones will also be heard when the key is struck and the piano strings vibrate. These overtones will occur at integer multiples of the fundamental frequency.
Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself).
Resonance
Resonance is the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force acting on a system is equal to (or close to) a natural frequency of the system. An oscillating force is applied at a resonant frequency of a system, causes oscillation at a higher amplitude than when an identical force is applied at non-resonant frequencies.
Resonant frequencies, also called resonance frequencies, are frequencies at which the response amplitude is a relative maximum. Small periodic forces near a resonant frequency of the system can produce large amplitude oscillations in the system due to the storage of vibrational energy.
Psychoacoustics is the branch of acoustics and psychophysics involving the scientific study of human sound perception and audiology; that is how humans perceive various sounds and the corresponding psychological responses.
Sound is mechanical radiant energy transmitted by longitudinal pressure waves in air and other materials; and as transverse waves in solids. Sound is the objective cause of hearing in humans and sounds that can be perceived include noise, speech and music.
Hearing is not a solely a mechanical phenomenon of sound wave propagation; rather it is also a sensory event and thus there are inherent human perceptions. The cochlea within the inner ear contains the cells responsible for perception. Mammals, including humans, have a coiled form of cochlea often called a mammalian cochlea. The outer hair cells of a mammalian cochlea provide enhanced sensitivity and frequency resolution. Nerve impulses then travel to the brain for perception.
Acoustics is the interdisciplinary science that deals with the study of mechanical waves propagating in gases (such as air), liquids, and solids including; mechanical waves include vibration, audible sound, ultrasound, and infrasound.
Psychophysics quantitatively studies the relationship between physical stimuli and the resulting sensations and perceptions. Psychophysics encompasses a general class of methods that can be applied to study a perceptual system. Modern applications rely heavily on threshold measurement, ideal observer analysis, and signal detection theory.
Psychophysicists typically design experimental stimuli that can be objectively measured; including pure tones varying in intensity, or lights varying in luminance. All the senses have been studied in the realm of psychophysics: vision, hearing, touch (including skin and enteric perception), taste, smell and the sense of time.
Psychoacoustics is the branch of psychophysics that studies hearing in response to audible stimuli. Sound waves propagating through air enter the ear and within the ear the sound is transformed into neural action potentials (nerve impulses). These nerve pulses then travel to the brain where sound perception occurs. Thus in the study of acoustics it is advantageous to take into account not just the mechanics of the environment; rather also to consider that both the ears and brain are involved in the listening experience.
Introduction (continued)
The human inner ear is signal processor that converts sound waves into neural stimuli; though sometimes differences in such sound waves are not perceptible. The ear has a non-linear response to sounds of different intensity levels.
Sound travels through air (and other mediums) in waves in three dimensions; however sound waves are often represented on two-dimensional graphs. Sound waves are generated by a sound source such as a vibrating diaphragm.
Frequency and Wavelength
Frequency, also called temporal frequency, is the number of occurrences of a repeating event per unit of time. The oscillations of sound waves are often characterized in terms of frequency; measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. The period is the duration (elapsed time) of one cycle in a repeating event, so the period is the reciprocal of the frequency.
Frequency is an essential concept used in science and engineering to study the rates of oscillatory and vibratory phenomena. For periodic waves, in cases where the wave speed is independent of frequency, a frequency, f, has an inverse relationship to the wavelength, λ.
Pitch is an auditory sensation related to frequency in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration.
Frequency is an objective, measurable scientific attribute; whereas pitch is each person's subjective perception of a sound wave (which cannot be directly measured). However, pitch is closely related to frequency, and it is almost entirely determined by frequency (not amplitude) with a high pitch corresponding to rapid oscillation and a low pitch corresponding to slow oscillation.
Sinusoidal Plane Waves
Sound waves are often simplified to a description in terms of sinusoidal plane waves, which are characterized by these generic properties:
- Frequency, or its inverse, wavelength
- Amplitude, sound pressure or intensity
- Speed of sound
- Direction
f = v / λ
Limits of Perception
The human ear can nominally hear sounds in the frequency range of 20 Hz to 20,000 Hz. The upper limit tends to decrease with age; most adults are unable to hear above 16,000 Hz (16 kHz). The lowest frequency that has been identified as a musical tone is 12 Hz under ideal laboratory conditions. Tones between 4 and 16 Hz are perceived via the body's sense of touch; and are rarely heard.
Frequency resolution of the ear is about 3.6 Hz within the octave of 1000–2000 Hz. That is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a repetitive variation in volume of the tone. This amplitude modulation occurs with a frequency equal to the difference in frequencies of the two tones and is known as beating.
Sound Pressure and Intensity
Sound pressure is the local pressure deviation from ambient pressure caused by a sound wave. The unit of measure of sound pressure is the pascal (Pa). The total pressure, PTOT is equal to the the static pressure, PSTAT, plus the sound pressure, P:
PTOT = PSTAT + P
Human hearing is sensitive to sound pressure which is related to sound intensity.
Sound intensity is the power carried by sound waves per unit area in a direction perpendicular to the area. The units of measure of sound intensity are watts per square meter (W/m2). Mathematically, sound intensity, I, is the product of the sound pressure, P, and the corresponding particle velocity, v:
I = Pv
Tone and Timbre
A pure tone is a sound with a sinusoidal wave form. A complex tone is a combination of two or more pure tones that have a periodic pattern of repetition (unless specified otherwise). A musical tone is a steady periodic sound characterized by duration, pitch, intensity (or loudness), and timbre.
Timbre is the perceived sound quality of a musical note, sound, or tone; and is what distinguishes musical instruments from one another when playing the same musical note at the same volume. Two instruments can sound equally tuned as they play the same note; yet while playing at the same amplitude, level each instrument will still sound distinctive. Each instrument will have its own unique timbre, also called tone color.
In music, the envelope is a description of how a sound changes over time and can relate to elements such as amplitude, frequency and pitch. The frequency spectrum and envelope are the physical characteristics of sound that determine timbre.
Harmonic Series
An overtone is any frequency greater than the fundamental frequency of a sound. The fundamental frequency and the overtones together are called partials. A piano key when struck is identified with a fundamental frequency corresponding to the intended musical note; however overtones will also be heard when the key is struck and the piano strings vibrate. These overtones will occur at integer multiples of the fundamental frequency.
Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself).
Resonance
Resonance is the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force acting on a system is equal to (or close to) a natural frequency of the system. An oscillating force is applied at a resonant frequency of a system, causes oscillation at a higher amplitude than when an identical force is applied at non-resonant frequencies.
Resonant frequencies, also called resonance frequencies, are frequencies at which the response amplitude is a relative maximum. Small periodic forces near a resonant frequency of the system can produce large amplitude oscillations in the system due to the storage of vibrational energy.