The speed of sound is not a fixed universal constant like the speed of light; it is highly dependent on the medium and the environmental conditions through which the sound waves travel. To address this variability, engineers and physicists developed the Mach number. The Mach number is a dimensionless ratio that compares an object’s velocity to the local speed of sound, providing a universal standard for motion, particularly in aerodynamics. This ratio converts the variable speed of sound into a useful benchmark for discussing high-speed travel.
The Physical Speed of Sound
The speed of sound, designated as \(V_{\text{s}}\), defines the rate at which a sound wave propagates through any elastic medium, such as air, water, or steel. Sound waves are mechanical vibrations, and their speed depends fundamentally on the stiffness and density of the material they travel through. The standard reference value is typically given for dry air at sea level under common conditions.
Under the specific conditions of dry air at a temperature of \(20^\circ\text{C}\) (or \(68^\circ\text{F}\)), sound travels at approximately \(343\) meters per second. This translates to an absolute speed of about \(1,235\) kilometers per hour or \(767\) miles per hour. This specific velocity serves as the baseline for calculating the Mach number in atmospheric flight.
The speed of sound is significantly different in other media because their molecular structures are much denser or stiffer than air. For instance, sound moves approximately \(4.3\) times faster in fresh water, traveling at about \(1,481\) meters per second at the same temperature. In a rigid solid like iron, sound can propagate at over \(5,120\) meters per second, which is nearly \(15\) times the speed it achieves in air.
Defining the Mach Number Ratio
The Mach number (\(M\)) is the ratio of an object’s true airspeed to the local speed of sound in the surrounding medium. This ratio measures compressibility effects in fluid flow, which become pronounced as an object approaches or exceeds the speed of sound. It is a dimensionless quantity, named after Austrian physicist Ernst Mach, who studied supersonic fluid dynamics.
The calculation is straightforward: \(M\) is the object’s velocity divided by the local speed of sound. When an aircraft travels at Mach 1, its speed equals the speed of sound at that specific altitude and temperature. This system allows engineers to discuss speed relative to a fluid dynamic threshold, rather than an arbitrary value that changes with altitude.
The Mach number provides a clear categorization of speed regimes in aerodynamics. Motion slower than the speed of sound, with a Mach number less than 1, is defined as subsonic. Flow at or near Mach 1 is known as transonic, a range where compressibility effects are most pronounced and complex. Speeds greater than Mach 1 are supersonic, and motion exceeding Mach 5 is categorized as hypersonic.
Environmental Factors Affecting Sound Speed
The velocity of sound is fundamentally dependent on the temperature and composition of the medium. For gases like air, temperature is the primary factor influencing sound speed; warmer air conducts sound faster than cooler air. As temperature increases, molecules gain kinetic energy and move more rapidly, allowing them to transmit sound vibrations more quickly through the gas.
The speed of sound in air increases by approximately \(0.6\) meters per second for every \(1^\circ\text{C}\) rise in temperature. This temperature dependence is why the speed of sound significantly decreases as an aircraft gains altitude, as the air temperature typically drops considerably in the troposphere. While pressure also changes with altitude, its effect on the speed of sound in an ideal gas is minimal; the dominant influence comes from the corresponding change in temperature.
Humidity also plays a small but measurable role, increasing the speed of sound. Water vapor molecules are lighter than the nitrogen and oxygen molecules that make up most of dry air. When water vapor replaces these heavier molecules, the overall density of the air slightly decreases, which allows sound waves to travel marginally faster.