The transmission of airborne sound between two rooms coupled by a panel is investigated. At low frequencies individual modes in the rooms and the panel control the transmission. It is shown that resonant modes in the room are the chief cause of frequency‐dependent variations in low‐frequency sound insulation. When the reception room has a dominant resonant mode the insulation is small or even negative. Similar behavior occurs when the panel has a dominant resonance but these effects occur at very low frequencies and if the panel is damped may not occur at all. A method is described by means of which the probable behavior of a given panel/room system can be predicted. General conclusions about the likely behavior of panels constructed of a range of materials are given.