Why Isn't the Speed of Sound Constant?
There is a concept that those interested in aviation or those who remember high school physics classes frequently encounter: "The speed of sound is 340 meters per second" (or about 1225 kilometers per hour). However, this statement is actually incomplete. The speed of sound is not an absolute value that remains constant in a vacuum or in every medium, like the speed of light. Since sound is a type of mechanical wave, it needs a material medium (air, water, metal, etc.) to travel. As the properties of the medium change, the speed of propagation of sound in that medium also changes.
For aircraft flying in the atmosphere, that is, in the air, the most critical and dominant factor determining the speed of sound is temperature. Air pressure or air density has no direct effect on the speed of sound (under the ideal gas assumption, changes in pressure and density cancel each other out). Therefore, in order to correctly calculate the Mach number (the ratio of an aircraft's speed to the speed of sound in that environment), we must know exactly the air temperature at the flying altitude.
The Direct Effect of Temperature on the Speed of Sound
Sound waves travel as air molecules collide with each other and transfer energy. When the air temperature rises, the kinetic energy of the molecules increases, meaning they move faster. The rapid movement of molecules allows sound waves to be transferred from one molecule to another faster. As a result:
- As temperature increases, the speed of sound increases.
- As temperature decreases, the speed of sound decreases.
According to ideal gas equations, the speed of sound in air is calculated by the following formula:
a = √(γ · R · T)
Here:
- a: Speed of sound (m/s)
- γ (Gamma): Specific heat ratio of air (approximately 1.4)
- R: Specific gas constant (approximately 287 J/(kg·K) for air)
- T: Absolute temperature (in Kelvin)
For practical calculations in aviation, this formula is usually adapted to sea-level standards. For faster and error-free results, you can use our Mach Number Calculator tool, enter the ambient temperature you are in, and see the current speed of sound and Mach value in seconds.
The Relationship Between Altitude and Mach Number
In the lowest layer of the Earth's atmosphere called the "Troposphere", where most weather events take place (up to about 11,000 meters or 36,000 feet altitude), the air temperature drops steadily as you go higher. According to the International Standard Atmosphere (ISA) model, the temperature decreases by approximately 2 degrees Celsius (or 1.98 °C) for every 1000 feet of ascent.
This situation brings a very important consequence for aviation: As the aircraft ascends, the air around it cools, and as the air cools, the speed of sound drops. Because the speed of sound drops, even if the aircraft's speed in kilometers/hour (or knots) remains constant, the Mach number it reaches increases.
A Striking Example
Let's assume the true airspeed (TAS) of a passenger plane is 900 kilometers per hour.
- At Sea Level (Temperature: 15°C): The speed of sound in this environment is approximately 1225 km/h. Our plane's Mach number is: 900 / 1225 = Mach 0.73.
- At 35,000 Feet Altitude (Temperature: -54°C): In this freezing cold, the speed of sound drops to approximately 1062 km/h. Even though our plane's speed is still 900 km/h, the Mach number is: 900 / 1062 = Mach 0.84.
As you can see, our plane flying at the same true speed became aerodynamically "faster" and got closer to the sound barrier simply because it flew in a higher and colder layer.
Practical Consequences and Warnings in Aviation
This physical reality leads to situations that pilots and aircraft designers must constantly consider:
1. Limiting Factors (Coffin Corner): A passenger plane flying at a high altitude must fly faster than its stall speed, but slower than the aircraft's structural maximum Mach (Mmo) limit. Because the speed of sound is lower at high altitudes, the Mmo limit is reached more easily. The safe flying speed range between these two limits (the narrowing band) is called the "Coffin Corner" in aviation.
2. Misconceptions: The question "What is the speed of sound in space?" is frequently asked. Because there is no air or other substance to transmit sound waves in space (a vacuum), there is no concept of the speed of sound. Therefore, it is technically meaningless to talk about a "Mach" value in space. The Mach number only applies to flights within the atmosphere (or within a fluid).
3. Test Flights: Maximum speed tests of newly designed aircraft are usually not conducted at very high altitudes, but at medium or low altitudes. Because at low altitude, the air is warm and the speed of sound is high. The plane can increase its true speed (in km/h) to much higher levels without crossing Mach 1 (the sound barrier), and its structural strength is tested.
Conclusion
Understanding the Mach number is possible not only by looking at the aircraft's speed dial but also by being able to read the thermometer outside. This unbreakable bond between temperature and the speed of sound is an invisible physical rule that shapes every stage of modern aviation, from flight planning to fuel calculations. Do not forget to add our Mach Number Calculator tool to your favorites to make your own calculations and see aerodynamic effects at different temperatures.
