An acoustic panel is provided that includes a first skin, a second skin and a cellular core. The first skin includes a plurality of perforations. The perforations are configured to provide the first skin with a percentage of open area that changes according to a non-linear function as the first skin extends in a first direction. Spacing between at least some of the perforations vary as the first skin extends in the first direction. The cellular core is arranged between and is connected to the first skin and the second skin. The cellular core includes a plurality of chambers. Each of the chambers extends between the first skin and the second skin. Each of the chambers is fluidly coupled with a respective one or more of the perforations.