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.
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An equivalent approach that might be more effective for algebra-based physics students is to use an approximation of the Doppler formula for low speeds12: where Δf is the Doppler shift and vR is the relative velocity between the observer and the source. From this equation and using the relative velocity corresponding to a stationary observer and an accelerated source the Doppler shift can be approximated as This equation is the same as Eq. (4) and can be derived without the use of calculus.
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2006
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