The pronounced interest in rotating detonation combustors (RDC) in recent years has witnessed the investigation of multiple facets of the combustor, like reactants, injection schemes and combustor geometry. The issue of instabilities in RDCs is a nascent field, and requires both the identification, and the subsequent explanation of different instability mechanisms. In particular, we are concerned with the low frequency instability exhibited by the detonation wave. This is attributed to two different types of low frequency instabilities amplitude and frequency modulated that are discovered in the air plenum of an RDC, and subsequently discussed. The occurrence of these instabilities is observed to depend on the fuel injection scheme used and the air flow rates through the combustor. The amplitude modulated instability in the air inlet is spatially varying, and rotates in a direction opposite to the direction of the detonation wave. At higher air flow rates, and thus higher pressure ratios across the air injection, this instability disappears. A preliminary hypothesis is proposed to explain this amplitude modulation. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.