Velocity of sound waves

Physically, the frozen sound velocity corresponds to the velocity of propagation of sound waves in a limit attained at high frequency, and the equilibrium sound velocity corresponds to the propagation velocity of sound waves in a limit attained at low frequency... 

Theoretical relationship of the elastic parameters with the velocities of sound waves... 

VanKrevelen-Hoftijzer viscosity-temperature relationship, 539 Van t Hoff equation, 751 Velocities of sound waves, 390 Velocity gradient, 526 Vertical Burning Test, 854 Vicat softening temperature, 849 Vickers hardness test, 837 Viscoelasticity, 405... 

Many problems in ultrasonic visualization, nondestructive evaluation, materials design, geophysics, medical physics and underwater acoustics involve wave propagation in inhomogeneous media containing bubbles and particulate matter. A knowledge of the effect of voids or inclusions on the attenuation and velocity of sound waves is necessary in order to properly model the often complex, multilayered systems. 

Another method for measuring mechanical properties on the macroscopic scale uses the relation between mechanical properties and the propagation of acoustic waves [89]. The velocity of sound waves and also the damping thereof can be directly deduced from the elastic and viscous properties. For polymers, ultrasound can be used since the damping of the acoustic waves is decreased at high frequencies. However, this method seems not to have been applied to fuel cell-related membrane materials so far. 

Velocity of sound Sound waves in air at normal temperatures and pressures (about 68°F [20°C] and 1 atmosphere pressure) travel at a velocity c that is approximately 1127 ft/s (344 m/s).The velocity of sound waves in air changes somewhat with temperature and pressure, but for most practical applications in plant engineering it can be considered a constant. Wavelength The distance that a sound wave travels in completing one cycle is the wavelength X and can be calculated at any frequency by ... 

The lattice dynamical method, which was originally proposed by Born and Huang [59], to calculate the velocity of sound waves in elastic solids and hence their elastic constants. The equation of motion of an atom is given by... 

It is common practice to measure elastic constants and their temperature dependence experimentally, either via static (e.g. three- or four-point bending, XRD or neutron scattering in connection with strain gauges) or via dynamic tests (e.g. sound velocity methods or resonant frequency techniques). It is well known from solid state physics, cf e.g. [Ashcroft Mermin 1976, Kittel 1988], that the elastic constants determine the velocity of sound waves in solids. For example, the velocity of transversal waves (shear waves) Vj, is given by... 

The best of all methods of measuring E is to measure the velocity of sound in the material. The velocity of longitudinal waves, v, depends on Young s modulus and the density, p ... 

This maximum velocity of a compressible fluid in a pipe is limited by the velocity of propagation of a pressure wave that travels at the speed of sound in the fluid [3]. This speed of sound is specific for each individual gas or vapor or liquid and is a function of the ratio of specific heats of the fluid. The pressure reduces and the velocity increases as the fluid flows downstream through the pipe, wdth the maximum velocity occurring at the downstream end of the pipe. WTien, or if, the pressure drop is great enough, the discharge or exit or outlet velocity will reach the velocity of sound for that fluid. 

If the velocity of the gas/fluid equals or exceeds the speed of sound, shock waves are set up, and vibrations and other mechanically related problems may result, compared to the conditions when velocities are below the speed of sound. For a Mach of 1.0, the gas velocity equals the velocity of sound in the fluid. 

The passage of a sound wave along a tube, so that no energy is dissipated by friction, is an example of a compressional wave of permanent type, and Newton applied his equation (1) to determine the velocity of sound in air. For this purpose he took e as the isothermal elasticity of air, which is equivalent to assuming that the temperature is the same in all parts of the wave as that in the unstrained medium. Since air is heated by compression and cooled by expansion, the assumption implies that these temperature differences are automatically annulled by conduction. Taking the isothermal elasticity, we have ... 

This equation gives for the velocity of sound in air at 0° 280 metres per second instead of 331, as obtained by experiment. The discrepancy was explained by Laplace (1822), who pointed out that in the sound wave the changes of volume are so rapid that the conditions are adiabatic, and not isothermal. Hence e = Q,... 

This value of uw corresponds closely to the velocity of sound in the fluid. That is, for normal conditions of transmission of a small pressure wave, the process is almost iscn-tropic. When the relation between pressure and volume is /V = constant, then ... 

It has been seen in deriving equations 4.33 to 4.38 that for a small disturbance the velocity of propagation of the pressure wave is equal to the velocity of sound. If the changes are much larger and the process is not isentropic, the wave developed is known as a shock wave, and the velocity may be much greater than the velocity of sound. Material and momentum balances must be maintained and the appropriate equation of state for the fluid must be followed. Furthermore, any change which takes place must be associated with an increase, never a decrease, in entropy. For an ideal gas in a uniform pipe under adiabatic conditions a material balance gives ... 

In the case of sound waves, which are of very low intensity, the pressure and density of the medium remain effectively constant throughout the process. Therefore, all parts of a sound wave are transmitted at the same velocity, so that a sinusoidal (sine) wave, for example, remains sinusoidal indefinitely during propagation. 

Thus, at J the velocity of the unbumed gases moving into the wave, that is, the detonation velocity, equals the velocity of sound in the gases behind the... 

Without going into detail with regard to this very interesting subject, it may be stated that "the velocity of the explosion wave in a gaseous mixture is nearly equal to the velocity of sound in iAe burning gases". 

On the basis of this relationship between the velocity of sound in the burning gases and the velocity of explosion, Professor H. B. Dixon calculated the velocity of the explosion wave in certain gaseous mixtures and also determined it experimentally, with the results gfiven below —... 

Combustion Wave of a Premixed Cos The velocity of sound in the burned gas is expressed by ... 

The lowest resonance frequency usually corresponds to the standing sound wave with longest wavelength. The velocity of sound c is... 

In examining the process of initiation of expls, ic is of importance to determine not only the critical density, p, and critical diameter, dc, of a detonator (or booster), but also its critical length, lc, which is the shortest length required for steady state detonation. It is known that if the initial velocity of shock wave of an initiator is equal to or lower than the velocity of sound, C0, in the charge to be initiated, no detonation can take place even with a large initiator. This means that the critical detonation velocity of an initiator, Dc, must be higher than a certain value which is different for each explosive to be initiated. Another requirement for successful detonation is that pressure at the front of a detonation wave produced by initiator at the expense of chemical energy, must be maintained at a certain minimum level... 

An exothermic chemical reaction that propagates with such rapidity that the rate of advance of the reaction zone into the unreacted material exceeds the velocity of sound in the unreacted material, that is the advancing reaction zone is preceded by a shock wave. The rate of advance of the reaction zone is termed detonation rate or detonation velocity. When this rate of advance attains such a value that it will continue without diminution thru the unreacted material, it is termed a stable detonation velocity. The exact value of this term is dependent upon a number of factors, principally the chemical and physical properties of the material. When the detonation rate is equal to or greater than the stable detona-... 

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