Revisiting Koehler's experiment of measuring the ratio of the specific heats of air by self-sustained oscillations

We revisit Koehler's experiment, a clever modification of Rüchardt's experiment designed to measure the ratio of specific heats of gas. However, the lengthy and dense analysis shared by Koehler in his 1950 paper may pose challenges to readers due to the complexity of the calculations. Following Koehler's approximation for pressure changes, we explicitly present the model equations as piecewise linear differential systems and qualitatively analyze the periodic solutions from a geometric perspective. This concise and transparent approach addresses a fundamental question about Koehler's experiment: why is the oscillation frequency nearly equal to the Rüchardt frequency? Our analysis avoids intricate calculations and should help educators introduce Koehler's experiment in general physics laboratory classes.