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A sensor was developed to quantitatively measure perturbations which change the volume of a wave chaotic cavity while leaving its shape intact. The sensors work in the time domain by using either scattering fidelity of the transmitted signals or time-reversal mirrors. The sensors were tested experimentally by inducing volume changing perturbations to a 1 m ^3 mixed chaotic and regular billiard system. Perturbations that caused a volume change that is as small as 54 parts in a million were quantitatively measured. These results were obtained by using electromagnetic waves with a wavelength of about 5 cm; therefore, the sensor is sensitive to extreme sub-wavelength changes of the boundaries of a cavity. The experimental results were compared with finite difference time-domain simulation results, and good agreement was found. Furthermore, the sensor was tested using a frequency-domain approach on a numerical model of the star graph, which is a representative wave chaotic system. These results open up interesting applications such as: monitoring the spatial uniformity of the temperature of a homogeneous cavity during heating up/cooling down procedures, verifying the uniform displacement of a fluid inside a wave chaotic cavity by another fluid, etc.