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In the plasma environment of a comet, waves are generated on vastly different temporal and spatial scales. Wave observations were carried out during the cometary flybys in the 1980s and 1990s as well as by the Rosetta spacecraft which accompanied comet 67P/Churyumov-Gerasimenko between 2014 and 2016. Waves are thought to contribute to the transfer of energy in the ionised coma. One of the fundamental plasma waves observed in space is the Langmuir wave, which appears at or above the electron plasma frequency. The Mutual Impedance Probe of the Rosetta Plasma Consortium (RPC-MIP) recorded frequency spectra of electric field fluctuations in the cometary plasma, and we used these spectra in order to detect and identify Langmuir waves. Langmuir waves were found during the part of the Rosetta mission when the comet was less than 2.65-2.8 AU from the Sun. The Langmuir waves appear near, but always outside, the diamagnetic cavity boundary, in a region where, at much lower frequencies, steepened magnetosonic waves also are present.