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Acoustic Impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cubic metre (), or in the MKS system the rayl per square metre (), while that of specific acoustic impedance is the pascal-second per metre (), or in the MKS system the rayl. There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electric current resulting from a voltage applied to the system. Mathematical definitions Acoustic impedance For a linear time-invariant system, the relationship between the acoustic pressure applied to the system and the resulting acoustic volume flow rate through a surface perpendicular to the direction of that pressure at its point of application is given by: : p(t) = * Qt), or equivalently by : Q(t) = * pt), where * ''p'' is the acoustic pressure; * ...
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Acoustic Pressure
Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) 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). Mathematical definition A sound wave in a transmission medium causes a deviation (sound pressure, a ''dynamic'' pressure) in the local ambient pressure, a ''static'' pressure. Sound pressure, denoted ''p'', is defined by p_\text = p_\text + p, where * ''p''total is the total pressure, * ''p''stat is the static pressure. Sound measurements Sound intensity In a sound wave, the complementary variable to sound pressure is the particle velocity. Together, they determine the sound intensity of the wave. ''Sound intensity'', denoted I and measured in W· m−2 in SI units, is defined by \mathbf I = p \mathbf v, where * ''p'' is the sound pressure, * v is the particle velocity. Acoustic ...
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Hilbert Transform
In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function, of a real variable and produces another function of a real variable . This linear operator is given by convolution with the function 1/(\pi t) (see ). The Hilbert transform has a particularly simple representation in the frequency domain: It imparts a phase shift of ±90° ( radians) to every frequency component of a function, the sign of the shift depending on the sign of the frequency (see ). The Hilbert transform is important in signal processing, where it is a component of the analytic representation of a real-valued signal . The Hilbert transform was first introduced by David Hilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions. Definition The Hilbert transform of can be thought of as the convolution of with the function , known as the Cauchy kernel. Because is not integrable across , the in ...
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Shear Modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackrel\ \frac = \frac = \frac where :\tau_ = F/A \, = shear stress :F is the force which acts :A is the area on which the force acts :\gamma_ = shear strain. In engineering :=\Delta x/l = \tan \theta , elsewhere := \theta :\Delta x is the transverse displacement :l is the initial length of the area. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M1L−1T−2, replacing ''force'' by ''mass'' times ''acceleration''. Explanation The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: * Young's modulus ''E'' describes the ...
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Solids
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural rigidity and resistance to a force applied to the surface. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire available volume like a gas. The atoms in a solid are bound to each other, either in a regular geometric lattice ( crystalline solids, which include metals and ordinary ice), or irregularly (an amorphous solid such as common window glass). Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because the molecules in a gas are loosely packed. The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids). Materials scien ...
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Bulk Modulus
The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli describe the material's response ( strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility. Definition The bulk modulus K (which is usually positive) can be formally defined by the equation :K=-V\frac , where P is pressure, V is the initial volume of the substance, and dP/dV denotes the derivative ...
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Fluids
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can be both fluid and solid. Viscoelastic fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers any liquid constituent of the body ( body fluid), whereas "liquid" is not used in this sense. Sometimes liquids given for flu ...
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Particle Displacement
Particle displacement or displacement amplitude is a measurement of distance of the movement of a sound particle from its equilibrium position in a medium as it transmits a sound wave. The SI unit of particle displacement is the metre (m). In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through air, the particle displacement is evident in the oscillations of air molecules with, and against, the direction in which the sound wave is travelling. A particle of the medium undergoes displacement according to the particle velocity of the sound wave traveling through the medium, while the sound wave itself moves at the speed of sound, equal to in air at . Mathematical definition Particle displacement, denoted δ, is given by :\mathbf \delta = \int_ \mathbf v\, \mathrmt where v is the particle velocity. Progressive sine waves The particle disp ...
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Speed Of Sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as well as the medium through which a sound wave is propagating. At , the speed of sound in air is about . The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior. In colloquial speech, ''speed of sound'' refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases, faster in liquids, and fastest in solids. For example, while sound travels at in air, it travels at in water (almost 4.3 times as fast) and at in iron (almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels at , ...
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Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different systems o ...
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Sound Pressure
Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) 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). Mathematical definition A sound wave in a transmission medium causes a deviation (sound pressure, a ''dynamic'' pressure) in the local ambient pressure, a ''static'' pressure. Sound pressure, denoted ''p'', is defined by p_\text = p_\text + p, where * ''p''total is the total pressure, * ''p''stat is the static pressure. Sound measurements Sound intensity In a sound wave, the complementary variable to sound pressure is the particle velocity. Together, they determine the sound intensity of the wave. ''Sound intensity'', denoted I and measured in W· m−2 in SI units, is defined by \mathbf I = p \mathbf v, where * ''p'' is the sound pressure, * v is the particle velocity. Acousti ...
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Intensive And Extensive Properties
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems. The terms ''intensive and extensive quantities'' were introduced into physics by German writer Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. An intensive property does not depend on the system size or the amount of material in the system. It is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, ''T''; refractive index, ''n''; density, ''ρ''; and hardness, ''η''. By contrast, extensive properties such as the mass, volume and entropy of system ...
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Particle Velocity
Particle velocity is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string. When applied to a sound wave through a medium of a fluid like air, particle velocity would be the physical speed of a parcel of fluid as it moves back and forth in the direction the sound wave is travelling as it passes. Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules, which depends mostly on the temperature an ...
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