On the speed of sound in the atmosphere as a function of altitude and frequency

Abstract

Sutherland and Bass (2004) have developed a calculation of the speed of sound and attenuation at altitudes up to 160 km. Dispersion is included in their treatment though emphasis is placed on absorption. That theory is explored in more detail to describe dispersion in the thermosphere. In the lower atmosphere, variations in the speed of sound with altitude are dominated by temperature and wind speed changes; the vibrational and rotational relaxation frequencies, which depend on the ratio of frequency to pressure (f/P), are in the kilohertz to megahertz range. As altitude increases, f/P and the mean free path increase, relaxation frequencies drop significantly, and velocity dispersion due to rotational and translational relaxation intensifies. This relaxation and resulting dispersion cause sound speeds at fixed frequencies to increase significantly with altitude, and to lower the altitude at which sound is refracted downward. Although the most extreme effects of dispersion are masked by simultaneously increased attenuation, decreases in traveltime of several percent are predicted at frequencies slightly below 1 Hz, demonstrating that this dispersion must be taken into account in order to correctly predict atmospheric returns at low frequencies. Copyright 2007 by the American Geophysical Union.