Sound speed defined

Sound is defined as any pressure variation that the human ear can detect. This variation can occur in air, water and other media. To determine noise, it is necessary to assess the frequency of the variation that, in turn, can be related to the speed. For most applications, the speed of sound is expressed at 340 meters per second... 

Now the assumption is dropped that the chemical reaction is a rate-controlled conversion to an invariant product composition, and the composition is permitted to vary with local thermodynamic state. Zel dovich, Brinkley Si Richardson, and Kirkwood Wood pointed out that since in a chemically reactive wave, pressure is a function not only of density and entropy but also of chemical composition, the sound speed for a reacting material should be defined as the frozen sound speed... 

As a means to compare directly 8p and 8u, we now introduce the pressure changes that are associated with velocity and density changes. It will be convenient to relate the fluid velocity to the sound speed as a measure of the magnitude of the velocity. By definition, the sound speed a is a property of the fluid defined as... 

In each case the attenuation of sound can be formally represented by defining a complex wavenumber, where the sound attenuation coefficient is the imaginary part of the wavenumber. The complex wavenumber also leads to the definition of a complex sound speed and a complex dynamic elastic modulus. 

The expression for the sound wave now has the same form, p = p exp[i(k x-cjt) ], as in a lossless medium. The complex wavenumber, substituted in Eg.4, defines a complex sound speed for the material as follows. 

For plane waves propigating in an isotropic homogeneous medium, three acoustic properties are important the speed of sound, the attenuation coefficient (to be discussed), and the characteristic impedance of the media. This impedance z is defined as the ratio of the acoustic pressure to the particle velocity associated with the wave motion in the material. For simple free-field plane waves, tliis is simply the product of the sound speed and density p. 

It was shown in Section 2.2 that the downstream Mach number is unity for Chapman-Jouguet waves. When interpreted correctly, this result applies to any combustible gas mixture. However, a possible source of ambiguity for multicomponent systems is the fact that more than one sound speed a can be defined. Since there are iV - - 2 independent thermodynamic variables in an AT-component gas mixture, N parameters besides s must be specified as constants in computing dp/dp to evaluate... 

A frozen (constant-composition) sound speed may be defined as... 

Keeping in mind that two-phase flows include both liquid-liquid systems and gas-liquid systems, the different behavior of a gas and liquid must be emphasized before discussing two-phase flows. The average distance between molecules in a gas phase is one order of magnitude higher than the diameter of its molecules, while it approaches the molecular diameter in a liquid phase. Therefore, in some microdevices the gas is compressed when the pressure strongly changes. The Mach number (Ma) is a dynamic measure of fluid compressibihty and is defined as the ratio of flow velocity (v) to sound speed (a) ... 

Choked flow also called critical flow is defined in single-phase flow as the flow when the fluid Mach number which is the ratio between the local fluid velocity and the local sound speed in the fluid approaches unity. For compressible single-phase flow or for gas-liquid two-phase flow when Mach number equal to one, the pressure gradient asymptotically... 

Other parameters, including the lattice sound speed Cs and weight factor fj, are lattice structure dependent. For example, for a typical D2Q9 (two dimensions and nine lattice velocities see Fig. 1) lattice structure, we have tQ = 4/9, ii 4 = 1/9, f5 8 = 1/36, and = A /3Afi, where Ax is the spatial distance between two nearest lattice nodes. Through the Chapman-Enskog expansion, one can recover the macroscopic continuity and momentum (Navier-Stokes) equations from the above-defined LBM dynamics ... 

The following typical combustion velocities have been observed the turbulent deflagration mode with a velocity of some dozens of meters per second in lean mixtures the sound deflagration mode, high-speed deflagration with 800-1,000 m/ s velocities, when the combustion front moves with the local sound speed relative to the reaction products the quasi-detonation mode when the velocity spectra exceeds 1,100 m/s, but is 200-500 m/s less than the CJ detonation velocity. The quasi-detonation mode velocity deficit, in comparison with thermodynamic defined values, is explained by impulse losses due to interactions with walls and obstacles. 

The quantity [u] is the relative molar increment of sound speed for a solute defined by the relation... 

There are certain limitations on the range of usefulness of pitot tubes. With gases, the differential is very small at low velocities e.g., at 4.6 m/s (15.1 ft/s) the differential is only about 1.30 mm (0.051 in) of water (20°C) for air at 1 atm (20°C), which represents a lower hmit for 1 percent error even when one uses a micromanometer with a precision of 0.0254 mm (0.001 in) of water. Equation does not apply for Mach numbers greater than 0.7 because of the interference of shock waves. For supersonic flow, local Mac-h numbers can be calculated from a knowledge of the dynamic and true static pressures. The free stream Mach number (MJ) is defined as the ratio of the speed of the stream (V ) to the speed of sound in the free stream ... 

Sound power is the total energy emitted from a fan that is a function of the fan s speed and point of operation and is independent of the fan s installation and surrounding environment Sound power level is the acoustical power expressed in decibels (dB) radiating from a source. Sound power can be converted into predictable pressure levels (dBA) after the acoustical environment surrounding the fan is defined. Sound pressure for a specific fan varies with... 

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

In accordance with the usual convention, we define a detonation as a reaction traveUing faster than the local speed of sound in the unreacted medium, and a deflagration as being a reaction travelling at or slower than the local speed of sound in the unreacted medium. An example of each type of event is given below ... 

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