The transformation of acoustic impedance can be accomplished either by a controlled variation of wavefront area as the wave progresses, or by transmission of the waves through a medium in which there is a gradient of density or elasticity. The second concept does not seem to have been exploited despite the fact that the effective density of a fluid medium can be increased by introducing suitable arrays of obstacles, and the bulk modulus of a liquid decreased by compliant inclusions. The present analysis shows that for plane waves a medium in which density varies as (B+mx)−2or elastic modulus as (B−mx)2, wherexis distance andBandmare constants, is analogous to the familiar exponential horn. Simple analytical solutions are also found for radial variations of density or elasticity which transform the behavior of sectoral and conical horns into the acoustic equivalents of exponential horns. Since the wave equation is separable in both cylindrical and spherical coordinates, these solutions are exact. Three examples of artificial fluid structure are given and the relationships between array size, bandwidth, and damping are discussed.