Speed of Sound & Standard Atmosphere

Your site and many others list the speed of sound as 761 mph, but an equal number of other sites say 742 mph. Which value is right? Why are they different?
- question from Gregory Levasseur
We are often asked about how fast the speed of sound is, and it is true that many sources give different answers. The heart of the problem is that speed of sound is not a fundamental property. It is calculated based upon other variables, namely temperature, and different sources may use different temperatures to calculate the speed of sound. In addition, the speed of sound is based on an approximation of the atmosphere called the standard atmosphere. This model is revised periodically to account for updated measurements of atmospheric properties. The value given by any particular reference may vary depending on whether it came from the 1958, 1962, 1966, or 1976 version of the standard atmosphere.

The above explanation, however, does not entirely address your question about where 761 mph (1,224 km/h) and 742 mph (1,194 km/h) come from. The difference rises from the fact that speed of sound changes depending on temperature. I found a good explanation of this difference in the following quote from a site that refers to the speed of sound as being 742 mph.

"The sound barrier is generally defined as 1,088 ft per second (about 742 mph) at sea level at 32°F. It varies in other temperatures and in different media."
Note that this site indicates that the 742 mph value assumes a temperature of 32°F (0°C). By comparison, the standard atmosphere that we use on our site is the 1976 version in which the temperature at sea level is assumed to be 59°F (15°C). As the above quote indicates, speed of sound changes with temperature. You can calculate this change using the following equation:

where

a = speed of sound [ft/s or m/s]
γ = specific heat ratio, which is usually equal to 1.4
R = specific gas constant, which equals 1716 ft-lb/slug/°R in English units and 287 J/kg/K in Metric units
T = atmospheric temperature in degrees Rankine (°R) in English units and degrees Kelvin (K) in Metric units
When using 32°F, or 492°R, in this equation, I calculate the speed of sound to be a little over 741 mph. By contrast, the standard atmospheric value of 59°F, or 519°R, produces a value of 761 mph.

Nevertheless, we still haven't answered the question as to which value is "right." In all honesty, it really comes down to a matter of opinion. It is for this reason that you have found such an even divide between sites that assume a value of 761 mph versus those assuming 742 mph. I would argue that 761 mph is the more accurate value since it is derived from the standard atmosphere. The standard atmosphere was developed for engineers who need a universally accepted reference for calculating atmospheric properties. These properties are critical in designing aircraft and predicting how they perform, so it is important for all designers to use the same reference.

Since atmospheric properties will vary at any given location on the Earth at any given time, it was necessary to develop an atmospheric model that approximates the conditions with sufficient accuracy to represent the actual atmosphere across the planet. In order to do so, scientists had to devise the so-called standard day. The conditions on this standard day represent an average between the extremes of different locations and seasons. The temperature on the average day was selected to be 59°F (15°C), and this temperature dictates the "standard" speed of sound. These conditions have been accepted as standard by engineers around the world so that aircraft designers in different countries can design their products to the same specifications. You can learn more about the standard day and standard atmosphere at these NASA sites:

Ultimately, the value that you accept as the speed of sound is really your decision. You may even prefer a different value than 761 mph or 742 mph depending on whether you live in a colder climate or a warmer climate. Keep in mind also that the difference between these two values is only about 2.5%, which is pretty insignificant in the grand scheme of things.
- answer by Jeff Scott, 25 January 2004

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