In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, attenuation (in some contexts, extinction) is the gradual loss of
flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ...
intensity through a
medium
Medium may refer to:
Science and technology
Aviation
* Medium bomber, a class of war plane
* Tecma Medium, a French hang glider design
Communication
* Media (communication), tools used to store and deliver information or data
* Medium ...
. For instance, dark
glasses
Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples ...
attenuate
sunlight
Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when ...
,
lead
Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, ...
attenuates
X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
s, and
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
and
air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
attenuate both
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
and
sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
at variable attenuation rates.
Hearing protectors help reduce
acoustic flux from flowing into the ears. This phenomenon is called
acoustic attenuation and is measured in
decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a ...
s (dBs).
In
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
and
telecommunication
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
s, attenuation affects the
propagation of waves and
signals in
electrical circuit
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage source ...
s, in
optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass ( silica) or plastic to a diameter slightly thicker than that of a human hair
Hair is a protein filament that grows ...
s, and in air.
Electrical attenuators and
optical attenuators are commonly manufactured components in this field.
Background
In many cases, attenuation is an
exponential function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, ...
of the path length through the medium. In optics and in chemical
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter ...
, this is known as the
Beer–Lambert law
The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied t ...
. In engineering, attenuation is usually measured in units of
decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a ...
s per unit length of medium (dB/cm, dB/km, etc.) and is represented by the attenuation
coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves ...
of the medium in question.
[Essentials of Ultrasound Physics, James A. Zagzebski, Mosby Inc., 1996.] Attenuation also occurs in
earthquake
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, fr ...
s; when the
seismic waves move farther away from the
hypocenter
In seismology, a hypocenter or hypocentre () is the point of origin of an earthquake or a subsurface nuclear explosion. A synonym is the focus of an earthquake.
Earthquakes
An earthquake's hypocenter is the position where the strain ener ...
, they grow smaller as they are attenuated by the
ground
Ground may refer to:
Geology
* Land, the surface of the Earth not covered by water
* Soil, a mixture of clay, sand and organic matter present on the surface of the Earth
Electricity
* Ground (electricity), the reference point in an electrical c ...
.
Ultrasound
One area of research in which attenuation plays a prominent role, is in
ultrasound
Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies ...
physics. Attenuation in ultrasound is the reduction in amplitude of the ultrasound beam as a function of distance through the imaging medium. Accounting for attenuation effects in ultrasound is important because a reduced signal amplitude can affect the quality of the image produced. By knowing the attenuation that an ultrasound beam experiences traveling through a medium, one can adjust the input signal amplitude to compensate for any loss of energy at the desired imaging depth.
[Diagnostic Ultrasound, Stewart C. Bushong and Benjamin R. Archer, Mosby Inc., 1991.]
*''Ultrasound attenuation'' measurement in
heterogeneous
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
systems, like
emulsion
An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Alth ...
s or
colloid
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend ...
s, yields information on
particle size distribution
The particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. Sig ...
. There is an ISO standard on this technique.
*''Ultrasound attenuation'' can be used for
extensional rheology measurement. There are
acoustic rheometer
An acoustic rheometer employs a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It applies an oscillating extensional stress to the system. System response can be interpreted in ter ...
s that employ
Stokes' law
In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. Stokes' law is derived by ...
for measuring
extensional viscosity and
volume viscosity.
Wave equations which take
acoustic attenuation into account can be written on a fractional derivative form.
[S. P. Näsholm and S. Holm, "On a Fractional Zener Elastic Wave Equation," Fract. Calc. Appl. Anal. Vol. 16, No 1 (2013), pp. 26–50,]
Link to e-print
/ref>
In homogeneous media, the main physical properties contributing to sound attenuation are viscosity and thermal conductivity.[G. Kirchhoff, "Ueber den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung", Ann. Phys. , 210: 177-193 (1868)]
Link to paper
/ref>[S. Benjelloun and J. M. Ghidaglia, "On the dispersion relation for compressible Navier-Stokes Equations,]
Link to Archiv e-printLink to Hal e-print
/ref>
Attenuation coefficient
Attenuation coefficient
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
s are used to quantify different media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency. The attenuation coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves ...
() can be used to determine total attenuation in dB in the medium using the following formula:
: