# How does altitude affect the speed of sound?

I read once that the speed of sound decreases as altitude increases. I wonder if that's true and, if so, are the pressure waves made at high altitude lesser than the ones at low altitude because of the difference in air pressure? And, lastly, does that mean that lower speeds at higher altitudes will be subject to the problems one encounters when approaching mach speed?

I read once that Mach speed decreases as altitude increases.

The speed of sound is solely dependant on temperature.

$$M = \sqrt{\gamma RT}$$

where $$\gamma$$ is the ratio of specific heats, $$R$$ is the molar gas constant and $$T$$ is the temprature in Kelvin. For Earth's athmosphere at 15° Celsius,

$$M=\sqrt{1.4\times 287\times 288.15}=340\,\text{m}/\text{s}$$

Does temprature decrease with altitude? Well, not always as can be seen by the international standard atmosphere:

....are the pressure waves made at high altitude lesser than the ones at low altitude because of the difference in air pressure?

There is no simple answer to this. Here's NASA's opinion:

Altitude determines the distance shock waves travel before reaching the ground, and this has the most significant effect on intensity. As the shock cone gets wider, and it moves outward and downward, its strength is reduced. Generally, the higher the aircraft, the greater the distance the shock wave must travel, reducing the intensity of the sonic boom. Of all the factors influencing sonic booms, increasing altitude is the most effective method of reducing sonic boom intensity.

• I edited the question a bit to make it more concise, hopefully it makes it a bit easier to answer... Also, I'm a little surprised, air density really has nothing to do with the speed of sound? – Jay Carr May 2 '14 at 19:49
• @JayCarr yep, even nasa says so :) grc.nasa.gov/www/k-12/airplane/Images/sound.gif – Thunderstrike May 2 '14 at 19:52
• @JayCarr only if you use the gas equation to substitute temperature with density and pressure :P – Federico May 2 '14 at 20:42
• @JanHudec I wouldn't say difficult, $p=\rho RT$ is one of the primitive equations we use to model the atmosphere. – casey May 2 '14 at 21:16
• And humidity? @MikeFoxtrot if the speed of sound depends also on the type of medium, wouldn't a different amount of humidity be a different medium? – maximusboscus Feb 10 '15 at 10:53