Mining volume measurement system

In a shaft with a curved or straight primary segment and smaller off-shooting segments, at least one standing wave is generated in the primary segment. The shaft has either an open end or a closed end and approximates a cylindrical waveguide. A frequency of a standing wave that represents the fundamental mode characteristic of the primary segment can be measured. Alternatively, a frequency differential between two successive harmonic modes that are characteristic of the primary segment can be measured. In either event, the measured frequency or frequency differential is characteristic of the length and thus the volume of the shaft based on length times the bore area.