The action of a cone in collecting sound coming in the direction of the axis may be investigated theoretically. If the diameter of the mouth be small compared with the wave-length (λ) of the sound, the cone may operate as a resonator, and the effect will vary greatly with the precise relation between λ and the length of the cone. On the other hand, the effect will depend very little upon the direction of the sound. It is probably more useful to consider the opposite extreme, where the diameter of the mouth is a large, or at any rate a moderate, multiple of λ, when the effect may be expected to fall off with rapidity as the obliquity of the sound increases.

A simple way of regarding the matter is to suppose the sound, incident axially, to be a pulse, e.g. a condensation confined to a narrow stratum bounded by parallel planes. If the angle of the cone be small, the pulse may be supposed to enter without much modification and afterwards to be propagated along. As the area diminishes, the condensation within the pulse must be supposed to increase. Finally the pulse would be reflected, and after emergence from the mouth would retrace its course. But the argument is not satisfactory, seeing that the condition for a progressive wave, i.e. of a wave propagated without reflection, is different in a cylindrical and in a conical tube.