We address vehicle classification and mensuration problems using acoustic and video sensors. In this paper, we show how to estimate a vehicle's speed, width, and length by jointly estimating its acoustic wave-pattern using a single passive acoustic sensor that records the vehicle's drive-by noise. The acoustic wave-pattern is approximated using three envelope shape (ES) components, which approximate the shape of the received signal's power envelope. We incorporate the parameters of the ES components along with estimates of the vehicle engine RPM and number of cylinders to create a vehicle profile vector that forms an intuitive discriminatory feature space. In the companion paper, we discuss vehicle classification and mensuration based on silhouette extraction and wheel detection, using a video sensor. Vehicle speed estimation and classification results are provided using field data.