Indonesian Caliphate
29. Mach and Sound Speed
Figures Mach ({\displaystyle \mathrm {Ma} }{\displaystyle \mathrm {Ma} } or {\displaystyle M}{\displaystyle M}) (spelled pronunciation: / ⁇ merk/, sometimes / ⁇ mex/ or / ⁇ maek/) is a common unit of speed for expressing the speed of an aircraft relative to the speed of sound. Units are usually placed before their measurement numbers such as Mach 1.0 for the speed of sound, Mach 2.0 for twice the speed of sound. The actual speed of sound depends on the atmospheric pressure and temperature. At 0°C air temperature and 1 atmospheric air pressure (atm), the speed of sound is 1,088 ft/s or 331.6 m/s or 748 mi/h.
Sound speed can be formulated with the equation {\displaystyle a\=20.047sqrt(T)}{\displaystyle a\=20.047sqrt(T)}, where T is the air temperature (K) and a is the sound speed (m/s). This equation applies to perfect gases.
Mach is not an abbreviation or acronym, but the name of an Austrian physicist named Ernst Mach (1838-1916), who in 1897 published an important scientific work on the basic principles of supersonic. Mach proposed a number to express the ratio of the velocity of an object to the speed of sound. Amazingly, he was the first to understand the principles of supersonic aerodynamics.
When an object (such as an airplane) penetrates the air, the air molecules near the plane are disturbed. If the aircraft is traveling at low speeds (generally less than 250 mph), the airspeed will remain . But at higher speeds, some of the aircraft's energy compresses the air and changes the local air density. This compressibility effect increases the amount of resultant force of the aircraft. This effect is increasingly important in line with the increase in speed.
When approaching or exceeding the speed of sound (about 330 m/s or 760 mph) a small disturbance in the airflow is channeled to another region under constant conditions. Large disruptions will affect the lift and drag of the aircraft. It can be said that the ratio of the speed of an object to the speed of sound in the air (gas) determines the effect of compressibility. Therefore the speed ratio becomes important and used as a parameter. Later aerodynamics called this parameter Mach (mach number). Mach number (M) allows to define the aircraft's "behavior" against the compressibility effect.
Interestingly, the use of Mach numbers was not introduced by Mach himself. The term was coined by Swiss engineer Jacob Ackeret in 1929. Mach himself did not name the number as Mach Number at that time. The word Mach was then used by people and at the same time as a tribute to Ernest Mach for his services to develop the basic principles of supersonic. Mach Angle (Mach Angle) and Mach Reflection in supersonic aerodynamics.
In the world of aviation, generally aircraft that have supersonic capabilities are fighter aircraft as well as F-16, MiG-29, MiG 25 or Rafale. Civilian aircraft are generally subsonic, except for the Concorde and the Tu-144 Concordski (the Russian version of the concorde). The Bell X-1A was the first aircraft to reach supersonic speeds of 1,650 mph (Mach 2.44) on December 12, 1953, by pilot Chuck Yeager.
The speed of sound is the term used to refer to the speed at which sound waves propagate in an elastic medium. At sea level, with a temperature of 20 °C (68 °F) and noral atmospheric conditions, the speed of sound is 343 m/sec (1238 km/h). The speed of propagation of these sound waves can differ depending on the medium through which they are passed (for example, sound is faster through water than air), the properties of the medium, and the temperature.
The speed of sound in an ideal gas depends only on its temperature and composition. Speed has a weak dependence on frequency and pressure in normal air, differing slightly from the ideal state.
In everyday speech, the speed of sound refers to the speed of sound waves in the air. However, the speed of sound varies from substance to substance: it is slowest in a gas; it is faster in a liquid; it is faster in a solid. For example, in air it is 343 m/s; in water 1,484 m/s (4.3 times); and in iron 5,120 m/s. In some very loud objects such as diamonds, sound propagates at a speed of 12,000 m/s; which is the maximum speed of sound under normal conditions.
Sound waves in a solid are composed of compression waves, and a type of sound wave called shear waves, which only appear on solid objects. Sliding waves in solid objects usually travel at different speeds, as shown in seismology. The speed of the compression wave in a solid is determined by compressibility, shear modulus, and density of the medium. The speed of the shear wave is determined only from the shear modulus and density of the solid material.
In fluid dynamics, the speed of sound in a liquid medium (gas or liquid) is used as a relative measurement for the speed at which objects move through the medium. The ratio between the speed of an object to the speed of sound in a fluid is called the Mach number. Objects that move beyond Mach 1 are called supersonic speeds.
The speed of sound in mathematical notation is denoted by c, from the Latin celeritas meaning "speed".
In general, the speed of sound c is expressed by the Newton–Laplace equation:
{\displaystyle c\={\sqrt {\frac {K_{s}}\rho {}},}}\displaystyle c\{=\sqrt {\frac {K_{{\rho }}{,}
with
Ks is the coefficient of hardness, the isentropic bulk modulus (or bulk elastic modulus for gases);
Thus the speed of sound increases directly proportional to the hardness of the material (the resistance of the elastic to deformation due to the force acting on the object) and is inversely proportional to the increase in density. For an ideal gas, the bulk modulus K is simply the gas pressure times the adiabatic index, which is 1.4 for air under normal pressure and temperature conditions.
For general equations of state, when classical mechanics is used, the speed of sound c is expressed by
{\displaystyle c\={\sqrt {\left({\frac {\partial p}{\partial \rho }}\right)_{s}}},}{\displaystyle c\=\sqrt {\left({\frac {\partial p}{\partial \rho }}\right)_{s}}},}
with
p is pressure;
⁇ is the density and the derivative is taken isentropically, then at constant entropy s.
If relativistic effects are important, then the speed of sound is calculated from the relativistic Euler equation.
In a non-dispersive medium, the speed of sound does not depend on the frequency of sound, so the speed of energy transport and sound propagation are the same for all frequencies. Air, a mixture of oxygen and nitrogen, forms a non-dispersive medium. However, air also contains a small portion of CO2, which is a dispersive medium, and causes dispersion into the air at ultrasonic frequencies (> 28 kHz).
In a dispersive medium, the speed of sound is a function of the frequency of sound, through a dispersion relationship. Each frequency component propagates at its own speed, called phase speed, while the energy of the disturbance propagates at group speed. The same phenomenon appears with light waves; see optical dispersion for explanation.
The approximate speed of sound in dry air (0% humidity), in meters per second, the temperature approaches 0 °C, can be calculated from
{\displaystyle c_{\mathrm {air} }\=(331.3+0.606\cdot \vartheta )~\mathrm {m/s} ,}{\displaystyle c_{\mathrm {air} }\=(331.3+0.606\cdot \varheta )~\mathrm {m/s} ,}
where {\displaystyle \vartheta }{\displaystyle \vartheta } is the temperature in degrees Celsius (°C).
This equation is derived from the first 2 terms of Taylor's expansion from the following equation:
{\displaystyle c_{\mathrm {air} }\=331.3~\sqrt {1{\frac +\vartheta {{273.15}{}\mathrm }m/s} .}{\displaystyle c_}\mathrm }air{ {\=331.3~{\sqrt {1+{\frac {\vartheta }273.15{}}\mathrm }m/s} .{
The value of 331.3 m/s, which produces a speed at 0 °C (or 273.15 K), is based on the theoretical value of heat capacity ratio, ⁇ , and, also the fact that at an air pressure of 1 atm can very well be explained by the approximate ideal gas. Some sound speed values at 0 °C can vary from 331.2 to 331.6 due to assumptions when counting. If the ideal gas ⁇ is assumed to be exactly 7/5 \= 1.4, then the speed of sound at 0 °C will produce the number 331.3 m/s.
This equation can be used for a wide temperature range, but still depends on the approximate heat capacity ratio, and for this reason cannot be used at very high temperatures. This formula will produce good predictions on relatively dry, cold, low pressure conditions, such as the Earth's stratosphere. This equation cannot be used for very low pressures and short wavelengths, due to its dependence on the assumption that the wavelength of sound in a gas is much longer than the average free distance between collisions of gas molecules.