Equations (5), (6) and (7) take the following form:
Eliminating and from here, we find the equation
This can be satisfied by the integral
(8)
in which , , , and are constants; substituting this integral into equation (8) and setting , we will find the relationship
Expression (8) represents a wave propagating
vertically at constant speed
but with varying amplitude. The speed of the sound under these circumstances is increased under the influence of gravity, but it is easy to see that this increase is negligible. So for example, taking the meter as the unit of length,