Speed of Sound and Mach 1

We get this question or variations thereof constantly. The subject was first addressed in a question we answered on how fast is Mach 2 in miles per hour. The conclusion of that explanation was that the speed of sound is not a constant value. Instead, it changes depending on how high up in the atmosphere you are and on the temperature.

To account for this behavior, aerospace engineers make use of what is called the standard atmosphere. This standard atmosphere is based on scientific atmospheric data collected at different locations within the atmosphere. This data was then used to create a series of equations that mathematically model the values of key atmospheric properties, such as temperature, density, and speed of sound. The results of this model provide engineers with "average" atmospheric properties on a so-called standard day.

The standard atmospheric model tells us that the speed of sound, or Mach 1, at sea level is:

However, this model assumes a "standard day" in which the air temperature is 59°F (15°C). If the actual temperature is higher, then the speed of sound will be higher as well. But the difference is small enough that we can neglect it for most engineering purposes, and the above values are accepted around the world as the speed of sound at sea level.

But now we face another problem, because aircraft do not typically spend much time flying at sea level. They instead cruise tens of thousands of feet above the Earth's surface where the speed of sound changes. This change in speed of sound is directly related to the change in temperature as altitude increases. This temperature change can be observed below.

Variation of temperature through the layers of the atmosphere
Variation of temperature through the layers of the atmosphere

Furthermore, the temperature (T) and speed of sound (a) are directly related by the following equation:

Having established that temperature changes with altitude and speed of sound is directly proportional to temperature, it is now clear that the speed of sound changes as altitude increases. As illustrated above, the temperature decreases at a linear rate up to about 11 km (6.8 mi) where the Tropopause begins. This region of the atmosphere is marked by constant temperature, and therefore constant speed of sound. The Tropopause extends up to about 20 km (12.4 mi), so the speed of sound does not change throughout this entire 9 km (5.6 mi) thick region. Scientific measurements and the standard atmospheric model have established that the speed of sound, or Mach 1, within this realm is:

Finally, we'd like to point out once again that the speed of sound at any altitude up to 280,000 ft (86,000 m) can be easily calculated using our Atmospheric Properties Calculator.
- answer by Jeff Scott, 10 November 2002

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