Man-made environments contain many mirrors and transparent objects, but it is difficult for robots to recognize transparent objects. To solve this issue, we use sound waves to recognize such hard-to-see objects. This research aimed to enable a robot to wipe a transparent window by estimating the azimuth angles of the window. To achieve this, we use a model-free learning method based on Support Vector Regression (SVR) to capture the features of the sound reflected from the target plane. To determine the input sound signal for the SVR, we derive a sound reflection model based on Shape-from-Shading in the computer vision field. Following this model, we use a sound property in the frequency domain recorded by a microphone as the input to the SVR. As a result of experiments using a transparent plate, in an anechoic chamber, we were able to estimate the azimuth angle within less than 3 degrees. As an example of a robot application using the method, we developed a robot wiping system that can handle such a transparent window. Even with such a realistic environment for the sensor system, we were able to estimate the azimuth angle within almost 5 degrees.