Millimeter Wave (mmWave) radar has emerged as a promising modality for speech sensing, offering advantages over traditional microphones. Prior works have demonstrated that radar captures motion signals related to vocal vibrations, but there is a gap in the understanding of the analytical connection between radar-measured vibrations and acoustic speech signals. We establish a mathematical framework linking radar-captured neck vibrations to speech acoustics. We derive an analytical relationship between neck surface displacements and speech. We use data from 66 human participants, and statistical spectral distance analysis to empirically assess the model. Our results show that the radar-measured signal aligns more closely with our model filtered vibration signal derived from speech than with raw speech itself. These findings provide a foundation for improved radar-based speech processing for applications in speech enhancement, coding, surveillance, and authentication.