The challenges of automated driving and driver assist systems increasingly require an enhanced sensing of the vehicle environment. Ultrasonic sensors are used especially in parking and maneuvering situations to calculate the distance to obstacles using the pulse-echo method. Because of their robustness, low production costs and widespread use, increasing the performance of ultrasonic sensors is of great interest. In this work, a processing pipeline and machine learning methods are examined for the purpose of a classification of obstacles using a single ultrasonic sensor. Raw time signals of ultrasonic echoes of typical objects in the vehicle environment are captured in a semi-anechoic chamber as well as on an asphalt parking space. Using the continuous wavelet transform, time-frequency images are extracted that are forwarded to a convolutional neural network. The classification of seven different object classes as well as the classification of traversability is performed. Promising results are achieved in classifying the traversability of obstacles. However, the discrimination of small objects can be challenging, especially on asphalt ground, which leads to interfering clutter reflections.