Page:On the influence of uneven temperature distribution on the propagation of sound.pdf/6



which, following the relations (1) take the form:

This must be accompanied by the condition of continuity, which, with the accepted degree of approximation, can be represented by the equation

Equations (5), (6) and (7) serve to determine small oscillation of gas under pressure and any external forces and under the influence of any temperature distribution.

§ 3. On the influence of gravity on vertically propagating plane sound waves.

Let us consider the vertical propagation of a plane sound wave in uniformly heated air, taking in account of the effects of gravity. Directing the $$x$$ axis vertically up and denoting the gravitational acceleration by $$g$$, we will have for the case under consideration,