High frequency combustion instabilities have plagued the development of liquid propellant rocket engines since their invention. Continuing research efforts aim to understand the mechanisms by which the oscillating combustion chamber pressure of self-sustaining combustion instabilities is driven. To this end, a rectangular combustor with acoustic forcing, designated 'BKH', was developed to study flame-acoustic interaction under conditions which are representative of real rocket engines. This article describes the acoustic characterisation of the BKH combustor using high frequency dynamic pressure measurements from the first hot-fire tests using liquid oxygen and ambient temperature or cryogenic hydrogen injectants. Analysis of the resulting high frequency pressure measurements shows excellent agreement with the predicted acoustic properties of the system which were calculated using finite element methods.