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In acoustics, a free field is a situation or space in which no sound reflections occur. [1] [2]
The lack of reflections in a free field means that any sound in the field is entirely determined by a listener or microphone because it is received through the direct sound of the sound source. This makes the open field a direct sound field. [3] In a free field, sound is attenuated with increased distance according to the inverse-square law. [1]
In nature, free field conditions occur only when sound reflections from the floor can be ignored, e.g. in new snow in a field, or approximately at good sound-absorbing floors (deciduous, dry sand, etc.) Free field conditions can be artificially produced in anechoic chambers. In particular, free field conditions play a major role in acoustic measurements and sound perception experiments as results are isolated from room reflections.
With voice and sound recordings, one often seeks a condition free from sound reflections similar to a free field, even when during post-processing specifically desired spatial impression will be added, because this is not distorted by any sound reflections of the recording room.
In the simple example shown in Figure 1, a singular sound source emits sound evenly and spherically with no obstructions. [1]
The sound intensity and pressure level of any point in a free field is calculated below, where r (in meters) is the distance from the source and "where ρ and c are the air density and speed of sound respectively. [1]
To calculate for air pressure, the equation can be written differently: [1]
In order to simplify this equation we can remove elements: [1]
Measuring the sound pressure level at a reference distance (Rm) from the source allows us measure another distance (r) more easily than other methods: [1]
This means that as the distance from the sources doubles, the noise level decreases by 6 dB for each doubling. However if the sound field is not truly free of reflections, a directivity factor Q will help "characterise the directional sound radiation properties of a source." [1]
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as
The Navier–Stokes equations are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes).
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 metres per second, or one kilometre in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating. At 0 °C (32 °F), the speed of sound in air is about 331 m/s. More simply, the speed of sound is how fast vibrations travel.
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson.
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).
Sound intensity, 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.
In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number , equal to the ratio of its pressure to its energy density :
Aeroacoustics is a branch of acoustics that studies noise generation via either turbulent fluid motion or aerodynamic forces interacting with surfaces. Noise generation can also be associated with periodically varying flows. A notable example of this phenomenon is the Aeolian tones produced by wind blowing over fixed objects.
In physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The form of the equation is a second order partial differential equation. The equation describes the evolution of acoustic pressure or particle velocity u as a function of position x and time . A simplified (scalar) form of the equation describes acoustic waves in only one spatial dimension, while a more general form describes waves in three dimensions. Propagating waves in a pre-defined direction can also be calculated using first order one-way wave equation.
Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration.
Acoustic waves are a type of energy propagation through a medium by means of adiabatic loading and unloading. Important quantities for describing acoustic waves are acoustic pressure, particle velocity, particle displacement and acoustic intensity. Acoustic waves travel with a characteristic acoustic velocity that depends on the medium they're passing through. Some examples of acoustic waves are audible sound from a speaker, seismic waves, or ultrasound used for medical imaging.
A bubble is a globule of one substance in another, usually gas in a liquid. Due to the Marangoni effect, bubbles may remain intact when they reach the surface of the immersive substance.
Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using full systems of governing equations of fluid dynamics and elasticity. These equations are generally nonlinear, and their traditional linearization is no longer possible. The solutions of these equations show that, due to the effects of nonlinearity, sound waves are being distorted as they travel.
Underwater acoustics or hydroacoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and 1 MHz. The propagation of sound in the ocean at frequencies lower than 10 Hz is usually not possible without penetrating deep into the seabed, whereas frequencies above 1 MHz are rarely used because they are absorbed very quickly.
In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the behavior of charged particles in a Coulomb potential and can be written in terms of confluent hypergeometric functions or Whittaker functions of imaginary argument.
The Minnaert resonance is a phenomenon associated with a gas bubble pulsating at its natural frequency in a liquid, neglecting the effects of surface tension and viscous attenuation. It is the frequency of the sound made by a drop of water from a tap falling in water underneath, trapping a bubble of air as it falls. The natural frequency of the entrapped air bubble in the water is given by
In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms, which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler can be measured by looking at the large scale structure of matter using astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy by constraining cosmological parameters.
In order to take a scientific measurement with a microphone, its precise sensitivity must be known. Since this may change over the lifetime of the device, it is necessary to regularly calibrate measurement microphones. This service is offered by some microphone manufacturers and by independent testing laboratories. Microphone calibration by certified laboratories should ultimately be traceable to primary standards a (National) Measurement Institute that is a signatory to International Laboratory Accreditation Cooperation. These could include the National Physical Laboratory in the UK, PTB in Germany, NIST in the USA and the National Measurement Institute, Australia, where the reciprocity calibration is the internationally recognised means of realising the primary standard. Laboratory standard microphones calibrated using this method are used in-turn to calibrate other microphones using comparison calibration techniques, referencing the output of the ‘test’ microphone against that of the reference laboratory standard microphone.
Transmission loss (TL) in duct acoustics describes the acoustic performances of a muffler-like system. It is frequently used in the industry areas such as muffler manufacturers and NVH department of automobile manufacturers, and in academic studies. Generally the higher transmission loss of a system it has, the better it will perform in terms of noise cancellation.
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