Exponential profile alone does not fix horn length, leaving design freedom

Evidence

Requiring that the horn increase its diameter (and likewise its area) exponentially does not specify how long it will be, even if we agree to a given diameter at the mouth. The length of the horn is controlled by the parameter L0. A long horn will naturally have a smaller rate of increase of diameter from one segment to the next. A colossal horn-that is, a long horn with a very large mouth-could indeed be a impressive instrument for addressing large numbers of people, as Athanasius Kircher claimed (see box 7. — Eric J. Heller, Why You Hear What You Hear- An…, 557