An acoustic sensing system to measure an interior characteristic of an object, for example, density, the presence of defects, or bond integrity (of a laminated object). The system includes a first set of acoustic transducers acting as transmitters for transmitting acoustic wave energy at a single frequency, which acoustic wave energy interacts with the object in a sensing region to provide transmitted, scattered, and reflected wave energy. A transmitter mounting mechanism allows the transmitters to be positioned in such a way that acoustic energy reflected from the object sets up a reverberation between the transmitter and the object. A second set of acoustic transducers acting as receivers of acoustic wave energy is positioned opposite the transmitters in such a way that acoustic waves passing through the object are coupled to the receivers. A second mounting mechanism allows the receivers to be similarly positioned such that acoustic energy passing through the object sets up a reverberation between the receiver and the object. A processor is connected to generate electrical control signals to the transmitter and to receive electrical signals from the receiver. The processor is operable to adjust the frequency of the electrical control signals to the transmitter in order to maintain a maximum of reverberation, and therefore a maximum of received signal at the receiver.