Speed of sound

The speed of sound plays an important role in the design of safety devices, as it determines the maximum possible flow rate of a fluid in case of a hazard. Furthermore, as a derivative property it has a considerable relevance for the adjustment of high-precision equations of state and for the indirect measurement of Cp, as explained in Section 3.2.4. 

Using these equations, the results for gases are usually sufficient. For liquids, a high-precision equation of state that describes the pressure-dependence of the liquid density is necessary. The expression for the speed of sound from high-precision equations of state formulated in terms of the Helmholtz energy (Eqs. (2.113) and (2.114)) is 

In air,. vSOLmd is approximately 330 m/sec. A common lecture trick involves speaking into a bag filled with a helium/oxygen mixture, which is breathable but raises the speed of sound dramatically compared to air (essentially a nitrogen/oxygen mixture)  

Since the speed rises while your voice box remains the same size, the frequency v =. vSoUndA of the sound disturbances you make goes up. As the sound exits the bag, it creates a pressure wave in the air with the same characteristic frequency (if the sound wave inside is hitting the wall of the bag 1000 times per second, the bag will vibrate a little 1000 times per second), and hence you hear a higher pitched note. 

---

Detonation. In a detonation, the flame front travels as a shock wave, followed closely by a combustion wave, which releases the energy to sustain the shock wave. The detonation front travels with a velocity greater than the speed of sound in the unreacted medium. 

The linear speed of sound in the Hquid is yi, B, and n are constants that should be set to the appropriate values for water. Any acoustic forcing function is included in the pressure at infinity term, (0- The pressure at the bubble wall, P(R), is given by... 

The flow velocity is thus proportional to the difference in transit time between the upstream and downstream directions and to the square of the speed of sound in the fluid. Because sonic velocity varies with fluid properties, some designs derive compensation signals from the sum of the transit times which can also be shown to be proportional to C. 

Compressible Vlow. The flow of easily compressible fluids, ie, gases, exhibits features not evident in the flow of substantially incompressible fluid, ie, Hquids. These differences arise because of the ease with which gas velocities can be brought to or beyond the speed of sound and the substantial reversible exchange possible between kinetic energy and internal energy. The Mach number, the ratio of the gas velocity to the local speed of sound, plays a central role in describing such flows. 

Increase Sound- Transmission Loss. The only significant iacreases ia sound-transmission loss that can be achieved by the appHcation of dampiag treatments to a panel occur at and above the critical frequency, which is the frequency at which the speed of bending wave propagation ia the panel matches the speed of sound ia air. AppHcation of dampiag treatment to 16 ga metal panel can improve the TL at frequencies of about 2000 H2 and above. This may or may not be helpful, depending on the appHcation of the panel. 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

Transport Properties. Viscosity, themial conductivity, the speed of sound, and various combinations of these with other properties are called steam transport properties, which are important in engineering calculations. The speed of sound (Fig. 6) is important to choking phenomena, where the flow of steam is no longer simply related to the difference in pressure. Thermal conductivity (Fig. 7) is important to the design of heat-transfer apparatus (see HeaT-EXCHANGETECHNOLOGy). The viscosity, ie, the resistance to flow under pressure, is shown in Figure 8. The sharp declines evident in each of these properties occur at the transition from Hquid to gas phase, ie, from water to steam. The surface tension between water and steam is shown in Figure 9. 

Fig. 6. Speed of sound in water and steam as a function of temperature. Values given correspond to pressures in MPa. To convert MPa to psi, multiply by...

Many special-purpose electrical thermometers have been developed, either for use in practical temperature measurement, or as research devices for the study of temperature and temperature scales. Among the latter are thermometers which respond to thermal noise (Johnson noise) and thermometers based on the temperature dependence of the speed of sound. 

Maeh Number and Speed of Sound The Maeh number M =... 

V/c is the ratio of fluid velocity to the speed of sound or aeoustie veloeity, c. The speed of sound is the propagation velocity of infinitesimal pressure disturbances and is derived from a momentum balance. The compression caused by the pressure wave is adiabatic and frictionless, and therefore isentropic. 

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number. 

A Free-stream speed of sound flexibility equation ... 

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 ... 

Factors of hardness, elasticity, toughness, and cleavage are important in determining grindabihty. Grindabihty is related to modulus of elasticity and speed of sound in the material [Dahlhoff, Chem. Ing. Tech., 39(19), 1112-1116 (1967)]. 

Explosions are either deflagrations or detonations. The difference depends on the speed of the shock wave emanating from the explosion. If the pressure wave moves at a speed less than or equal to the speed of sound in the unreacted medium, it is a deflagration if it moves faster than the speed of sound, the explosion is a detonation. 

Deflagration to Detonation Transition A reaction front that starts out with velocities below the speed of sound and subsequently accelerates to velocities higher than the speed of sound in the unreacted material is said to have undergone a Deflagration to Detonation Transition. The possibility of transition is enhanced by confinement/turbulence generators in the path of the reaction front. 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

In Chapter 13 we showed that, if a material contains a crack, and is sufficiently stressed, the crack becomes unstable and grows - at up to the speed of sound in the material -to cause catastrophically rapid fracture, or fast fracture at a stress less than the yield stress. We were able to quantify this phenomenon and obtained a relationship for the onset of fast fracture... 

---