A flexible membrane is attached to an internal wall of the fairing of a flight vehicle. The membrane is inflated with gas to achieve a shape that couples with and thereby attenuates the first acoustic resonance occurring within the volume enclosed by the fairing. A sensor senses the varying ambient atmospheric pressure during flight. A pressure regulating system includes an inflation valve and pressure relief valve. Based on the sensed ambient atmospheric pressure, this system adjusts the membrane's gauge pressure throughout the flight trajectory to maintain the desired coupling gauge pressure. Acoustic blankets can also be attached to the internal walls of the fairing to abate resonances having frequencies greater than 500 Hz. Inflating the membrane with helium enhances the attenuation otherwise obtained. Multiple membranes can be individually tuned to respectively attenuate multiple acoustic resonances.