An acoustic panel is provided that includes a perforated first skin, a second skin and a corrugated structure. The corrugated structure is between and is connected to the perforated first skin and the second skin. The corrugated structure includes a first baffle, a first septum, first material and second material that is configured with the first material. The first baffle is formed by an uninterrupted portion of the first material. The first septum is formed by a portion of the second material that is exposed through an interruption in the first material.