Abstract
In our papers(1) on the interpretation of the anomalous propagation of sound waves. especially at a short distance, we have studied the effect of the current of the air, on an idealized assumption that there is an uniform current in each of the two layers of the air respectively. In the present short note, we studied the sound waves which is transmitted through the air with current varying as the height, on the assumption that the velocity of the current is small compared with the sound velocity and that the temperature is constant. If we define P such that the variable part of the density ρ'=DP, the fundamental equation can be written in the form (D2=c2Δ)P=O,
where D=∂/∂t+U ∂/∂x, c is the velocity of sound when there is no current and ΔLaplacian, the z-axis being taken vertically upwards and x-, y- axes horizontally. U is the velocity of the current and a function of z. In the case in which U varies linearly as the height z, In the case in which U varies linearly as the height z, we obtain a solution which involves a cylindrical function of degree 1/3. It corresponds to the plane waves when the current is uniform. The ray of sound bends in the course of its propagation, as one can expect from the outset. Our former idealized theory must be filled up in this respect, but the essential idea is not affected because the bend is small as the present investigation shows.
