Systems and methods for sound damping in air conditioning systems in an aircraft is provided. In one embodiment, an air conditioning conduit can comprise a sound-damping wall that at least partially encloses a continuous hollow space for guiding the air. The wall comprises a multilayer design with a core layer and at least one first cover layer. The core layer comprises a sound-absorbing open-pore core material so that the wall shows an acoustic effect. The first cover layer is airtight, is arranged on the external surface of the core layer, and is two-dimensionally connected to the core layer. The two-dimensional connection between the core layer and the first cover layer causes a composite effect in such a manner that the wall is self-supporting and has a structural function in order to be able to transfer mechanically-occurring loads to structural parts of the aircraft.