The speed of a torsional stress wave transmitted in a solid waveguide, that has a non-circular cross-section and is submerged in a liquid, is inversely proportional to the density of the liquid. Thus, by measuring the speed of the torsional stress wave, one can obtain information about the liquid's density or density-related characteristics such as liquid level and the mass composition of bi-phase mixtures. A predictive theory is developed to correlate the speed of the wave with the liquid's density and the shape of the waveguide's cross-section. The theory is used to optimize the waveguide's geometry so as to increase the sensor's sensitivity. The theoretical results are compared and found to favorably agree with experimental observations.