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Psychoacoustics Fundamentals

AudioStudies

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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:
  • Frequency, or its inverse, wavelength
  • Amplitude, sound pressure or intensity
  • Speed of sound
  • Direction
In dispersive situations wherein the wave speed varies with frequency, the frequency of a sinusoidal save is equal to the phase velocity, v of the wave divided by the wavelength:

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.
 
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AudioStudies

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Thread Starter #2
Room Curve Targets

Double-blind listening tests conducted for decades have conclusively shown that listeners prefer loudspeakers with a flat frequency response, with no sudden changes in frequency response (a smooth response). The flat frequency response is desired with respect to anechoic on-axis and listening-window situations. If the room curve is flat the sound will be too bright (exhibit exaggerated high frequencies). Thus if a loudspeaker measures flat in an anechoic chamber, the response will not be flat in a typical listening room.

The sound pressure level (SPL) at a given distance from a loudspeaker often varies at different angles even though the distance is the same. This phenomena is called directionality. A loudspeaker’s directivity is the changes in level associated with direction.

Loudspeakers with smoothly changing or relatively constant directivity perform best. When such loudspeakers are measured in reflective listening rooms the steady-state room curves exhibit a smooth downward tilt. This downward tilt is attributable to the frequency-dependent directivity of standard (cone/dome) loudspeakers. These loudspeakers are omnidirectional at low bass frequencies, becoming progressively more directional as frequency rises.

More energy is radiated at low than at high frequencies. Standard loudspeakers tend to show a gently rising directivity index (DI) with frequency. Well-designed horn loudspeakers exhibit quite constant DI over their operating frequency range. There is no evidence that either standard loudspeaker designs or horn loudspeakers are advantageous; as both are highly rated by listeners.

Room curves for the aforementioned loudspeakers exhibit a downward tilted line with a slight depression around 2 kHz, attributable to the nearly universal directivity discontinuity at the woofer/midrange-to-tweeter crossover. The small dip should not be equalized because equalization alters the perceptually dominant direct sound.
 
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AudioStudies

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Amplitude and Frequency Response

Humans can hear and respond to sound intensities of a tremendous range, from barely audible sounds at midrange frequencies to those that are uncomfortably loud at higher frequencies. Lower bass frequencies are felt as vibrations, rather than heard. A logarithmic scale is used to depict sound pressure level (SPL) because of this tremendous range. The units of measure are decibels (dB).

The amplitude of a sound is the strength or level, typically measured in SPL. The SPL is used to compare absolute levels of different sounds. With respect to loudspeakers, SPL measurements are used to determine sensitivity, the SPL at the standard distance of one meter and the standard voltage of 2.83 volts.

The SPL is related to the amplifier power of amplifiers that power speakers. Twice as much amplifier power is required to produce a 3 dB increase in the SPL. Due to the logarithmic scale, a 10 dB increase in SPL requires ten times more power from the amplifier.

Of paramount importance in audio is the frequency response curve that depicts the amplitude versus frequencies in the audible range. Audio engineers use a family of curves that is informally called the spinorama to evaluate loudspeakers and room acoustics.

Loudness is the human perception correlated with SPL; however it also depends on frequency, incident angle, duration of the sound, and the temporal envelope. Bass (lower frequency) sounds must be much higher in SPL to be perceived by humans as loud as midrange frequencies and high frequencies.
 
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AudioStudies

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Thread Starter #4
Loudspeakers and Psychoacoustics

Introduction

Loudspeaker design is both an art and a science, and the science part has advanced rapidly in recent decades. The artists who design truly great loudspeakers do not violate the science, or at least their designs pose no serious violations. Physics, most simply defined, is the basic laws of nature, and as such is the most fundamental science related to loudspeaker design. The performance of any loudspeaker depends first and foremost on the basic laws of nature, regardless of how complex a loudspeaker system may appear.

The quest for the perfect loudspeaker will always be a quest. There are no perfect loudspeakers, just as there are no perfect automobiles, or perfect people. Nevertheless there are the fundamental physics and engineering principles applicable to the quest towards the flawless loudspeaker.
With the science and technology available today or likely in the near future, perfection cannot be achieved in a loudspeaker design. However, the journey towards such perfection is worthwhile and can lead to the design and subsequent construction of higher quality loudspeakers.

The physics precursor dictates that there will always be compromises in the design of loudspeakers. However, ignoring the relevant physics can result in a loudspeaker substantially more compromised than it needs to be, and often undesirable for playing music. Certain characteristics of loudspeakers appear to enhance the delivery of good sound in a variety of listening rooms. Good sound will not be achieved with poorly designed loudspeakers.

The performance of loudspeakers is affected not only by the speaker design, but other factors such as the placement of the speakers within the room, the position of the listener with respect to the speakers, the shape and size of the room, and even to some extent the furnishings in the room. The loudspeakers, room and listener form a system that determines attributes of the listening experience.

Loudspeakers cannot be optimized without knowing certain physical properties of the room wherein the sound is propagated to the listener. Likewise, the listening room cannot be optimized without knowing properties of the loudspeaker. A knowledge of how humans perceive sound (psychoacoustics) helps in the process of optimizing of listening rooms to the best extent possible. However, it is not possible for every factor to be fully considered; as there are no perfect loudspeakers and no perfect listening rooms. However, evaluation and design criteria are available that can increase the chances of obtaining good sound in normal listening environments.

Transducers and Cone Parameters

Many scientific principles applied to engineering design involve energy transformations. This energy transfer occurs commonly in many of the things we use every day. Consider that a car battery converts chemical energy to electrical energy. A ceiling fan converts electrical energy to mechanical energy. Energy transformations occur in loudspeakers, wherein electrical, mechanical, and acoustical energy are relevant considerations, as well as heat loss.

A transducer is a device for converting energy from one form to another form. Engineering applications related to audio require the use of transducers. Examples of transducers related to audio applications include:

Microphones: devices that convert sound energy to electrical energy
Loudspeaker drivers: devices that convert electrical energy to sound energy

Parameters typically used to design and evaluate cone loudspeakers are listed in the table below.

Displacement Volume VD
Driver Motor Strength Bl
Effective Driver Radiating Area Sd
Equivalent Compliance Volume Vas
Efficiency (free air reference) ηo
Free Air Resonance (Driver) fs
Electrical Q (Driver) Qes
Mechanical Q (Driver) Qms
Total Driver Q Qts
Mass of speaker cone assembly Mmd
Voice Coil Overhang xmax
 
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Thread Starter #5
The directivity of a loudspeaker represents the changes in sound pressure level (SPL) associated with direction. Sound power is the rate at which sound energy is emitted, reflected, transmitted or received, per unit time. The unit of measure of sound power is the Watt (W).

The directivity index (DI) corresponds to the difference between direct sound and reflected sound within a room; and is an indicator of the difference in decibels between the on-axis sound and the total radiated sound power. Standard loudspeakers tend to show a gently rising DI with increases in frequency.

Dispersion of radiated sounds within a listening room varies with frequency and is dependent on the size of the radiating surface(s). The size of the low frequency driver, typically a woofer or subwoofer, is of paramount importance with respect to directivity.

Low frequencies typically radiate in an omnidirectional manner due to their long wavelengths in comparison with the source size. For these audio playback situations of low frequencies, the directly index, DI, is near zero. With respect to most sources, as the frequency increases, so does the directivity; thus the reflections decrease. The higher the DI, the greater the level of direct sound relative to reflections arriving at the listening position.

Loudspeakers designed with flat on-axis frequency responses exhibit a rising sound power output at lower frequencies (with some exceptions for unique designs). Thus typically listeners are exposed to more prolific reflected sound at low frequencies than at high frequencies.

With respect to tweeters, there is a reduction in DI as the angular dispersion of a high frequency horn expands; and this is reduced further with a small dome tweeter in the domestic loudspeaker.
 
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Thread Starter #6

Acoustics of Small Rooms

Introduction

Sound waves from point sources in air, if unimpeded, exhibit spherical propagation; and this situation is considerably simpler than sound fields typically generated in listening rooms. The walls of the room and furnishings in the room impede sound waves, and can either absorb or reflect sound, depending on the nature of the impediment and the frequencies of sound from the sources (loudspeakers).

The audible spectrum for humans is generally considered to be between the frequencies of 20 Hz and 20,000 Hz (20 kHz), and there is a significant difference in wavelengths within this range. At 20 Hz the wavelength of sound is 56.5 feet; whereas at 20 kHz the wavelength is 0.0565 ft. Clearly, with respect to the lower frequencies, the wavelengths exceed the dimensions of small listening rooms. Modal resonance effects dominate at low frequencies.

Ballou (1) identifies that for convenience the audible spectrum can be divided into four regions:
  • Region X: a very low frequency region, wherein no modal effects can occur;
  • Region A: a low frequency region dominated by normal modes;
  • Region B: an intermediate frequency region dominated by diffraction and diffusion;
  • Region C: a higher frequency region dominated by specular reflection.
The frequencies bounding these regions can be calculated for a given room if the room dimensions and reverberation time are known. The lowest modal frequency separates region X from region A and is calculated as the speed of sound, 1130 ft/s , divided by twice the room length, 2L:

fLM = 1130 / 2L

The boundary between region A and region B can be estimated from an equation that Ballou (1) attributes to McKay(2):

fAB = 11250 SQRT(RT/V)

where RT is reverberation time in seconds, and V is the room volume in cubic feet.

The boundary frequency between region B and region C is four times fAB :

fBC = 4 fAB

There is no acoustical analysis pertinent to region X. Analysis in region A is based on wave acoustics. Region B is a transition region with unique characteristics. Acoustical analysis in Region C is based on ray acoustics (similar to light).

Room Size Considerations

The smaller the room, the higher the transition frequency (1130 / 2L) between region X and region A and this results in less desirable low frequency response. Region A increases as the room volume is reduced; thus more frequencies will be dominated by modal resonances. According to Ballou1:

“It also means greater spacing of modal frequencies resulting in irregularity of room response and increasing colorations of sound.”

Smaller rooms are also less desirable for region B, which also increases in size, as the room volume decreases.

References
  • 1. Ballou, Glen (Editor), “Handbook for Sound Engineers” – 1st ed., 3rd printing (1988)
  • 2. McKay, R. L. “In a Synergetic Audio Concepts LEDE” – (1982)
 
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