Ion acoustic waves were observed between 15 and 30 km from the centre of comet 67P/Churyumov–Gerasimenko by the Rosetta spacecraft during its close flyby on 28 March 2015. There are two electron populations: one cold at kBTe≈0.2 eV and one warm at kBTe≈2 eV. The ions are dominated by a cold (a few hundredths of electronvolt) distribution of water group ions with a bulk speed of (3–3.7) km s−1. A warm kBTe≈6 eV ion population, which also is present, has no influence on the ion acoustic waves due to its low density of only 0.25 % of the plasma density. Near closest approach the propagation direction was within 50∘ from the direction of the bulk velocity. The waves, which in the plasma frame appear below the ion plasma frequency fpi≈2 kHz, are Doppler-shifted to the spacecraft frame where they cover a frequency range up to approximately 4 kHz. The waves are detected in a region of space where the magnetic field is piled up and draped around the inner part of the ionised coma. Estimates of the current associated with the magnetic field gradient as observed by Rosetta are used as input to calculations of dispersion relations for current-driven ion acoustic waves, using kinetic theory. Agreement between theory and observations is obtained for electron and ion distributions with the properties described above. The wave power decreases over cometocentric distances from 24 to 30 km. The main difference between the plasma at closest approach and in the region where the waves are decaying is the absence of a significant current in the latter. Wave observations and theory combined supplement the particle measurements that are difficult at low energies and complicated by spacecraft charging.