## 23 September 2009

### Speed of Sound

Does the speed of sound change with elevation?

Yes it does is the short answer but because I learned from my father that is never the way to answer here are the details.

The basic formula for finding the speed of sound is:
$c = \sqrt {\kappa \cdot R\cdot T}$

• R (287.05 J/(kg·K) for air) is the gas constant for air
• κ (kappa) is the adiabatic index (1.402 for air)
• T is the absolute temperature in kelvins
As can be seen by this the only thing that changes is temperature. As the temperature is lower the speed of sound is slower. This is the primary reason that sound is slower at higher elevations, the air is cooler there.

Just some examples the speed of sound at sea level is about 760 miles per hour and it is about 660 miles for an airplane.

Now what about sound through a solid object?

The stiffness and density of the material will affect the speed. Stiffness will will increase the speed and density will slow it down. This can make the calculations complicated. Here is the basic formula used to calculate the speed through solid materials:
$c = \sqrt{\frac{C}{\rho}}$
C is a coefficient of stiffness
ρ is the density
There are other variations of this formula to calculate for liquids and gases.

Most of the information for this post was obtained from:

http://en.wikibooks.org/wiki/Acoustics/Sound_Speed

http://www.engineeringtoolbox.com/speed-sound-d_82.html

There is also a great slide show that has some examples and video of sound and speed: http://www.slideshare.net/darrella/speed-of-sound