Absorption

FIELDS OF STUDY: Acoustics; Electromagnetism

ABSTRACT: The mechanisms by which acoustic and electromagnetic waves carry energy are briefly described. Absorption is the transfer of energy from a wave to the medium through which it propagates. Absorption is one main component of wave attenuation, the other being scattering. Each material has a unique absorption coefficient that characterizes how much energy it can absorb from a sound or light wave.

Principal Terms

• absorption coefficient: a value characteristic of a particular medium that represents the amount of light or sound it absorbs from a wave passing through it.
• acoustics: the study of sound; also, the qualities of a space that affect how sound is heard within that space.
• albedo: the portion of electromagnetic energy that is reflected when its waves encounter a surface or boundary; often used to describe solar radiation reflecting off Earth or another body in space.
• attenuation: the loss of energy from a wave passing through a medium due to absorption or scattering.
• Beer-Lambert law: a formula that relates the attenuation of an electromagnetic wave in a given medium to the thickness of that medium and the concentration of attenuating materials within it.
• light wave: an oscillation in an electromagnetic field.
• reflection: the rebounding of a wave from a surface or boundary between two mediums, causing it to travel back through the original medium.

Wave Energies

Energy comes in many different forms. Some types of energy, such as sound energy and radiant energy, travel in the form of waves. Sound energy is kinetic energy that is carried by sound waves, also called acoustic waves. Sound waves are a type of mechanical wave, meaning that they travel, or propagate, by oscillating the molecules of the surrounding medium. A mechanical wave must have a medium in order to propagate.

Radiant energy is the energy carried by electromagnetic radiation, which travels in the form of electromagnetic waves. These waves are sometimes called light waves because visible light is a kind of electromagnetic radiation. However, the electromagnetic spectrum extends far beyond the range of visible light. Electromagnetic waves do not require a medium, although the presence of one can influence how they propagate. Instead, they travel as oscillations in the electromagnetic field. This is why light can travel through the vacuum of space.

Different types of waves share a number of common physical properties. For example, all waves have a wavelength, frequency, and amplitude. Wavelength is the distance between identical points on two successive wave cycles. Frequency is the number of wave cycles per unit time. Amplitude is the distance between a wave’s highest point (crest) and its lowest point (trough).

In addition, all waves experience reflection, refraction, diffraction, and interference. Reflection occurs when a wave bounces off a boundary between two mediums and changes direction. In the case of radiant energy, albedo refers to the amount of waves that are reflected. Refraction is a change in wave direction caused by the wave passing through the boundary rather than rebounding from it. Diffraction occurs when a wave bends around an obstacle or spreads out after passing through a small opening. Interference is the superposition of two or more waves to form a single wave with an amplitude equal to the sum of those of the contributing waves at the points where they meet.

Acoustic and electromagnetic waves are also subject to scattering and absorption. Scattering occurs when a portion of a wave’s energy is reflected by irregularities in the medium. Absorption is the transfer of energy from a wave into the medium through which it is traveling. The medium takes up energy from the wave and transforms it into another kind of energy, such as heat.

Energy and Matter

Energy is observed and measured in terms of its effects on matter. When an acoustic wave passes through matter, the sound energy pushes its particles together, forming an area of compression, or increased particle density. Once the wave is no longer exerting pressure, this creates an area of rarefaction, or decreased particle density, just behind the area of compression. The rarefaction allows the compressed particles to return to their original position. These back-and-forth movements of particles are the oscillations that make up an acoustic wave. As they oscillate, the particles bump into each other, producing friction. The heat generated by this friction is sound energy that has been absorbed by the medium and transformed.

If light is directed in a beam through a medium, the energy of the beam can be measured on both sides of the medium and compared. The amount of energy transmitted per unit time is called "radiant power" or "radiant flux." It is measured in watts (W), the International System of Units (SI) derived unit of power. One watt is equal to one joule of energy transmitted per second (J/s). Transmitted radiant flux (φ_t) is the amount of radiant flux that exits a medium. The initial radiant flux (φ_i) is the amount that entered the medium. The ratio between the transmitted and initial radiant flux produces a value known as the transmittance (T):

Transmittance can be used to calculate both the attenuance (D) of a material and its optical depth (τ):

D = −log₁₀T

τ = −lnT

Attenuance measures the radiant flux lost to attenuation. Optical depth is the opacity of a material to electromagnetic radiation. The function ln is the natural logarithm, or log_e, where e is the mathematical constant known as Euler’s number, roughly equal to 2.71828. The relationship between transmittance, absorbance, and optical depth can also be expressed using the inverse functions of the logarithms:

T = e⁻τ = 10⁻D

There is some debate over the use of the term "attenuance" versus "absorbance." The quantity defined here as attenuance is also commonly called absorbance (A), even though it measures energy lost by scattering as well as absorption. The International Union of Pure and Applied Chemistry (IUPAC) has recommended using "absorbance" only when attenuation due to scattering is negligible or otherwise not taken into account. Transmittance calculated using absorbance alone is known as "internal transmittance," as opposed to total transmittance:

A = −log₁₀T_int

T_int = 10⁻A

Attenuation and Absorption Coefficients

A wave may pass through a medium with little to no interaction. Or, it may lose some or all of its energy to that medium. This loss of energy is called "attenuation." It results in a decrease in the wave’s intensity, or its power per unit area.

The two main components of attenuation are scattering and absorption, both of which depend on the characteristics of the medium. A given material is characterized by an attenuation coefficient (μ). This unique value represents how easily the material can be penetrated by a wave. Just as attenuation is the sum total of energy lost to scattering and to absorption, a material’s attenuation coefficient is the sum of its scattering coefficient and its absorption coefficient.

For electromagnetic waves, one usually specifies either a molar absorption coefficient or a linear absorption coefficient. The molar absorption coefficient (ε) is typically used in chemical analysis of solutions. It relates absorbance (A) to path length (l)—that is, the distance the wave travels through the medium—and the concentration (c) of absorbing materials in the medium, as described by the Beer-Lambert law:

A = εcl

The linear absorption coefficient (a) is defined as the absorbance (A) per unit path length (l):

For acoustic waves, the absorption coefficient (α) of a material is the ratio of absorbed sound intensity (I_a), in watts per meter squared (W/m²), to initial sound intensity (I_i):

Its value ranges from 0 (no sound absorbed) to 1 (all sound absorbed). This value can be used to calculate the total sound absorption (A) of either a single surface or an enclosure of multiple surfaces, such as a room, according to the following equation:

A = α₁S₁ + α₂S₂ + . . . + αnSn

Here, S is the surface area of a given material, and A is measured in sabins. The sabin, named after American physicist Wallace Clement Sabine (1868–1919), is a unit of sound absorption equal to the absorbing ability of a quantity of material with an absorption coefficient of 1. It can be either metric (one square meter of completely absorbing material) or imperial (one square foot), depending on whether S is measured in meters or feet squared.

Applications of Absorption

Electromagnetic absorption is an important factor in numerous fields. In medicine, x-ray imaging works because different tissues absorb different amounts of x-rays; in meteorology, temperature is affected by the absorption of solar radiation by Earth’s atmosphere and surface. In chemistry and materials science, the Beer-Lambert law can be used to identify unknown solutions.

Acoustic absorption is an everyday concern for architects, engineers, and anyone else who designs buildings or other structures where sound propagation is an issue. An engineer may want to design a recording studio with soundproofed booths or an auditorium that can project sound to distant audience members. In either case, it is necessary to use materials with appropriate absorption coefficients. The studio material should have a higher coefficient, to prevent sound from entering from outside. The auditorium material should have a lower coefficient, to increase the reverberation time of sound from the stage. Engineers who deal with acoustics frequently consult tables showing the absorption coefficients of common building materials.

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