Calculating “g” from Acoustic Doppler Data

Traditionally, the Doppler effect for sound is introduced in high school and college physics courses. Students calculate the perceived frequency for several scenarios relating a stationary or moving observer and a stationary or moving sound source. These calculations assume a constant velocity of the observer and/or source. Although seldom discussed in this context, generalization of the Doppler effect for accelerated sound sources is relatively straightforward and can be used as an enriching tool in the classroom. The purpose of this paper is to describe a simple experiment to determine the acceleration of gravity (g) from an acoustic source in free fall. The Doppler effect is usually applied to scenarios where the relative velocity between a sound-emitting object and an observer is nonzero or when the perceived and real sound frequencies are known and a specific speed is unknown.1 Sometimes a combined equation can be used in which the user changes positive and negative signs depending on the relative motions of the sound-emitting object and the observer. That is,