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The horizontal axis shows frequency in Hz Lindos1.svg
The horizontal axis shows frequency in Hz

In acoustics, loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud." [1] The relation of physical attributes of sound to perceived loudness consists of physical, physiological and psychological components. The study of apparent loudness is included in the topic of psychoacoustics and employs methods of psychophysics.

Acoustics science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound

Acoustics is the branch of physics that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.

Subjectivity is a central philosophical concept, related to consciousness, agency, personhood, reality, and truth, which has been variously defined by sources. Three common definitions include that subjectivity is the quality or condition of:

Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone. The SI unit of sound pressure is the pascal (Pa).


In different industries, loudness may have different meanings and different measurement standards. Some definitions, such as ITU-R BS.1770 refer to relative loudness of different segments of electronically reproduced sounds, such as for broadcasting and cinema. Others, such as ISO 532A (Stevens loudness, measured in sones), ISO 532B (Zwicker loudness), DIN 45631 and ASA/ANSI S3.4, have a more general scope and are often used to characterize loudness of environmental noise.

Loudness, K-weighted, relative to full scale (LKFS) is a loudness standard designed to enable normalization of audio levels for delivery of broadcast TV and other video. Loudness units relative to full scale (LUFS) is a synonym for LKFS that was introduced in EBU R128. Loudness units (LU) is an additional unit used in EBU R128. It describes Lk without direct absolute reference and therefore describes loudness level differences.

The sone is a unit of loudness, how loud a sound is perceived. Doubling the perceived loudness doubles the sone value. Proposed by Stanley Smith Stevens in 1936, it is not an SI unit.

Karl Eberhard Zwicker was a German acoustics scientist and full professor at the Technical University of Munich.

Loudness, a subjective measure, often confused with physical measures of sound strength such as sound pressure, sound pressure level (in decibels), sound intensity or sound power. Filters such as A-weighting and LKFS attempt to compensate measurements to correspond to loudness as perceived by the typical human.

The decibel is a unit of measurement used to express the ratio of one value of a power or field quantity to another on a logarithmic scale, the logarithmic quantity being called the power level or field level, respectively. It can be used to express a change in value or an absolute value. In the latter case, it expresses the ratio of a value to a fixed reference value; when used in this way, a suffix that indicates the reference value is often appended to the decibel symbol. For example, if the reference value is 1 volt, then the suffix is "V", and if the reference value is one milliwatt, then the suffix is "m".

Sound intensity level also known as acoustic intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (W/m2). One application is the noise measurement of sound intensity in the air at a listener's location as a sound energy quantity.

Sound power or acoustic power is the rate at which sound energy is emitted, reflected, transmitted or received, per unit time. It is defined as "through a surface, the product of the sound pressure, and the component of the particle velocity, at a point on the surface in the direction normal to the surface, integrated over that surface." The SI unit of sound power is the watt (W). It relates to the power of the sound force on a surface enclosing a sound source, in air. For a sound source, unlike sound pressure, sound power is neither room-dependent nor distance-dependent. Sound pressure is a property of the field at a point in space, while sound power is a property of a sound source, equal to the total power emitted by that source in all directions. Sound power passing through an area is sometimes called sound flux or acoustic flux through that area.


The perception of loudness is related to sound pressure level (SPL), frequency content and duration of a sound. [2] The relationship between SPL and loudness of a single tone can be approximated by Stevens's power law in which SPL has an exponent of 0.67. [lower-alpha 1] More precise measurements, a model known as the Inflected Exponential function, [3] indicate that loudness increases with a higher exponent at low and high levels and with a lower exponent at moderate levels. [4]

Stevens's power law is an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the stimulus. It is often considered to supersede the Weber–Fechner law, based on a logarithmic relationship between stimulus and sensation, because the power law describes a wider range of sensory comparisons.

The sensitivity of the human ear changes as a function of frequency, as shown in the equal-loudness graph. Each line on this graph shows the SPL required for frequencies to be perceived as equally loud, and different curves pertain to different sound pressure levels. It also shows that humans with normal hearing are most sensitive to sounds around 2–4 kHz, with sensitivity declining to either side of this region. A complete model of the perception of loudness will include the integration of SPL by frequency. [5]

Equal-loudness contour

An equal-loudness contour is a measure of sound pressure, over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours. By definition, two sine waves of differing frequencies are said to have equal-loudness level measured in phons if they are perceived as equally loud by the average young person without significant hearing impairment.

Historically, loudness was measured using an "ear-balance" audiometer in which the amplitude of a sine wave was adjusted by the user to equal the perceived loudness of the sound being evaluated. Contemporary standards for measurement of loudness are based on summation of energy in critical bands. [6]

Audiometer machine used for evaluating hearing acuity

An audiometer is a machine used for evaluating hearing acuity. They usually consist of an embedded hardware unit connected to a pair of headphones and a test subject feedback button, sometimes controlled by a standard PC. Such systems can also be used with bone vibrators, to test conductive hearing mechanisms.

The amplitude of a periodic variable is a measure of its change over a single period. There are various definitions of amplitude, which are all functions of the magnitude of the difference between the variable's extreme values. In older texts the phase is sometimes called the amplitude.

In audiology and psychoacoustics the concept of critical bands, introduced by Harvey Fletcher in 1933 and refined in 1940, describes the frequency bandwidth of the "auditory filter" created by the cochlea, the sense organ of hearing within the inner ear. Roughly, the critical band is the band of audio frequencies within which a second tone will interfere with the perception of the first tone by auditory masking.

Hearing loss

When sensorineural hearing loss (damage to the cochlea or in the brain) is present, the perception of loudness is altered. Sounds at low levels (often perceived by those without hearing loss as relatively quiet) are no longer audible to the hearing impaired, but sounds at high levels often are perceived as having the same loudness as they would for an unimpaired listener. This phenomenon can be explained by two theories, called loudness recruitment and softness imperception.

Loudness recruitment posits that loudness grows more rapidly for certain listeners than normal listeners with changes in level. This theory has been accepted as the classical explanation.

Softness imperception, a term coined by Mary Florentine around 2002, [7] proposes that some listeners with sensorineural hearing loss may exhibit a normal rate of loudness growth, but instead have an elevated loudness at their threshold. That is, the softest sound that is audible to these listeners is louder than the softest sound audible to normal listeners.


The "loudness" control associated with a loudness compensation feature on some consumer stereos alters the frequency response curve to correspond roughly with the equal loudness characteristic of the ear. [8] Loudness compensation is intended to make the recorded music sound more natural when played at a lower levels by boosting low frequencies, to which the ear is less sensitive at lower sound pressure levels.


Loudness normalization is a specific type of audio normalization that equalizes perceived level such that, for instance, commercials do not sound louder than television programs. Loudness normalization schemes exist for a number of audio applications.


Movie and home theaters

Music playback


Historically Sone (loudness N) and Phon (loudness level L) units have been used to measure loudness. [10]

A-weighting follows human sensitivity to sound and describes relative perceived loudness for at quiet to moderate speech levels, around 40 phons.

Relative loudness monitoring in production is measured in accordance with ITU-R BS.1770 in units of LKFS. [11]

Work began on ITU-R BS.1770 in 2001 after 0 dBFS+ level distortion in converters and lossy codecs had become evident; and the original Leq(RLB) loudness metric was proposed by Gilbert Soulodre in 2003. [12] Based on data from subjective listening tests, Leq(RLB) compared favorably to numerous other algorithms. CBC, Dolby and TC Electronic and numerous broadcasters contributed to the listening tests.

Loudness levels measured according to the Leq(RLB) specified in ITU-R BS.1770 are reported in LKFS units.

The ITU-R BS.1770 measurement system was improved for made multi-channel applications (monaural to 5.1 surround sound). To make the loudness metric cross-genre friendly, a relative measurement gate was added. This work was carried out in 2008 by the EBU. The improvements were brought back into BS.1770-2. ITU subsequently updated the true-peak metric (BS.1770-3) and added provision for even more audio channels, for instance 22.2 surround sound (BS.1770-4).

See also


  1. The relationship between loudness and energy intensity of sound can therefore be approximated by a power function with an exponent of 0.3.

Related Research Articles

Weighting filter

A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes.

A noise weighting is a specific amplitude-vs.-frequency characteristic that is designed to allow subjectively valid measurement of noise. It emphasises the parts of the spectrum that are most important.

The phon is a unit of loudness level for pure tones. Human sensitivity to sound is variable across different frequencies; therefore, although two different tones may have identical physical intensities, they may be psychoacoustically perceived as differing in loudness. The purpose of the phon is to provide a standard measurement for perceived intensity. The phon is psychophysically matched to a reference frequency of 1 kHz. In other words, the phon matches the sound pressure level (SPL) in decibels of a similarly perceived 1 kHz pure tone. For instance, if a sound is perceived to be equal in intensity to a 1 kHz tone with an SPL of 50 dB, then it has a loudness of 50 phons, regardless of its physical properties. The phon was proposed in DIN 45631 and ISO 532 B by S. S. Stevens.

Sound quality

Sound quality is typically an assessment of the accuracy, fidelity, or intelligibility of audio output from an electronic device. Quality can be measured objectively, such as when tools are used to gauge the accuracy with which the device reproduces an original sound; or it can be measured subjectively, such as when human listeners respond to the sound or gauge its perceived similarity to another sound.

Absolute threshold of hearing

The absolute threshold of hearing (ATH) is the minimum sound level of a pure tone that an average human ear with normal hearing can hear with no other sound present. The absolute threshold relates to the sound that can just be heard by the organism. The absolute threshold is not a discrete point, and is therefore classed as the point at which a sound elicits a response a specified percentage of the time. This is also known as the auditory threshold.

A weighting curve is a graph of a set of factors, that are used to 'weight' measured values of a variable according to their importance in relation to some outcome. An important example is frequency weighting in sound level measurement where a specific set of weighting curves known as A, B, C and D weighting as defined in IEC 61672 are used. Unweighted measurements of sound pressure do not correspond to perceived loudness because the human ear is less sensitive at low and high frequencies, with the effect more pronounced at lower sound levels. The four curves are applied to the measured sound level, for example by the use of a weighting filter in a sound level meter, to arrive at readings of loudness in Phons or in decibels (dB) above the threshold of hearing..

In digital and analog audio, headroom refers to the amount by which the signal-handling capabilities of an audio system exceed a designated nominal level. Headroom can be thought of as a safety zone allowing transient audio peaks to exceed the nominal level without damaging the system or the audio signal, e.g., via clipping. Standards bodies differ in their recommendations for nominal level and headroom.

Audiogram type of graph showing audiometer results

An audiogram is a graph that shows the audible threshold for standardized frequencies as measured by an audiometer. The Y axis represents intensity measured in decibels and the X axis represents frequency measured in hertz. The threshold of hearing is plotted relative to a standardised curve that represents 'normal' hearing, in dB(HL). They are not the same as equal-loudness contours, which are a set of curves representing equal loudness at different levels, as well as at the threshold of hearing, in absolute terms measured in dB SPL.

Sound level meter

A sound level meter is used for acoustic measurements. It is commonly a hand-held instrument with a microphone. The diaphragm of the microphone responds to changes in air pressure caused by sound waves. That is why the instrument is sometimes referred to as a Sound Pressure Level (SPL) Meter. This movement of the diaphragm, i.e. the sound pressure deviation, is converted into an electrical signal.

Psophometric weighting

Psophometric weighting refers to any weighting curve used in the measurement of noise. In the field of audio engineering it has a more specific meaning, referring to noise weightings used especially in measuring noise on telecommunications circuits. Key standards are ITU-T O.41 and C-message weighting as shown here.

Loudspeaker measurement

Loudspeaker measurement is the practice of determining the behavior of loudspeakers by measuring various aspects of performance. This measurement is especially important because loudspeakers, being transducers, have a higher level of distortion than other audio system components used in playback or sound reinforcement.

PEAQ is a standardized algorithm for objectively measuring perceived audio quality, developed in 1994-1998 by a joint venture of experts within Task Group 6Q of the International Telecommunication Union's Radiocommunication Sector (ITU-R). It was originally released as ITU-R Recommendation BS.1387 in 1998 and last updated in 2001. It utilizes software to simulate perceptual properties of the human ear and then integrates multiple model output variables into a single metric. PEAQ characterizes the perceived audio quality as subjects would do in a listening test according to ITU-R BS.1116. PEAQ results principally model mean opinion scores that cover a scale from 1 (bad) to 5 (excellent).

Dialnorm is the metadata parameter that controls playback gain within the Dolby Laboratories Dolby Digital (AC-3) audio compression system. Dialnorm stands for dialog normalization. Dialnorm is an integer value with range 1 to 31 corresponding to a playback gain of -30 to 0 dB (unity) respectively. Higher values afford more headroom and are appropriate for dynamic material such as an action film.

Auditory masking occurs when the perception of one sound is affected by the presence of another sound.


A-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured sound levels in an effort to account for the relative loudness perceived by the human ear, as the ear is less sensitive to low audio frequencies. It is employed by arithmetically adding a table of values, listed by octave or third-octave bands, to the measured sound pressure levels in dB. The resulting octave band measurements are usually added to provide a single A-weighted value describing the sound; the units are written as dB(A). Other weighting sets of values – B, C, D and now Z – are discussed below.

Psychoacoustics is the scientific study of sound perception and audiology – how humans perceive various sounds. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound. It can be further categorized as a branch of psychophysics. Psychoacoustics received its name from a field within psychology—i.e., recognition science—which deals with all kinds of human perceptions. It is an interdisciplinary field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.

Mary Florentine is a Matthews Distinguished Professor at Northeastern University., specialising in psychoacoustics with interests in models of hearing, non-native speech comprehension in background noise, cross-cultural attitudes towards noise, and hearing loss prevention. Her primary collaborator is Søren Buus.


  1. American National Standards Institute, "American national psychoacoustical terminology" S3.20, 1973, American Standards Association.
  2. Poulsen, Torben (1981). "Loudness of tone pulses in a free field". The Journal of the Acoustical Society of America. 69: 1786. Bibcode:1981ASAJ...69.1786P. doi:10.1121/1.385915.
  3. Goldstein, E. Bruce (2009). Encyclopedia of Perception Vol. 1. Sage. p. 147. ISBN   9781412940818.
  4. Florentine, Mary; Epstein, Michael (2006). "To honor Stevens and repeal his law". Proceedings of the International Society for Psychophysics. 22.
  5. Olson, Harry (1972). "The Measurement of Loudness". Audio Magazine.
  6. As described in IEC 532, DIN 45631 and ASA/ANSI S3.4
  7. Mary Florentine (March 2003), It's not recruitment-gasp!! It's softness imperception, 56 (3), Hearing Journal, pp. 10, 12, 14, 15, doi:10.1097/01.HJ.0000293012.17887.b4
  8. Lenk, John D. (1998). Circuit Troubleshooting Handbook. McGraw-Hill. p. 163. ISBN   0-07-038185-2.
  9. EBU Recommendation R 128: Loudness normalisation and permitted maximum level of audio signals (PDF), European Broadcasting Union, August 2011, retrieved 2013-04-22
  10. Olson, Harry F. (February 1972). "The Measurement of Loudness" (PDF). Audio: 18–22.
  11. Recommendation BS.1770, International Telecommunication Union, August 2012, retrieved 2013-05-31
  12. "Leq Meter" . Retrieved 2015-12-15.