Aircraft speed and height from Doppler-shifted sound and flight-track data

The changing pitch of a passing aircraft is a familiar example of the Doppler effect. We use audio recordings of 40 aircraft passages to estimate the speed and height by two methods based on the Doppler effect. The endpoint method is an analytical model that uses the limiting frequencies at the start and end of each recording and the slope near the middle of the frequency-time curve. The second method fits the whole curve. Results from both methods are compared with independent flight-tracking data. The endpoint method consistently underestimates speed and height because the recorded frequencies have not approached their limiting values. The full curve fit agrees with the tracking data within about 3% in speed and 12% in height for steady passages, with poorer agreement when speed or height changes. Software developed with AI assistance made it practical to analyze this many passages. The comparison offers undergraduate students an example of testing model assumptions and identifying systematic errors in real measurements.