Calculating g from Acoustic Doppler Data

Abstract

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.

Direct quantitative measurements of Doppler effects for sound sources with gravitational acceleration

“…In this experiment, we let a sound source fall freely towards a microphone and measure the time dependence of the frequency. The experiment is similar in spirit to some previous experiments 9,10 , though more quantitative. To obtain the experimental results, we start recording on the PC and let the voice recorder drop (attached to a line to avoid it dropping all the way).…”

“…Since practical considerations are of import, we provide the details of the experiment, such as the parameters and the equipment used. Due to its significance as a fundamental physics phenomenon, various forms of Doppler effect experiments have been proposed and conducted for some time: Doppler effect due to a wave source on a toy car 1 , on an air track 2,3,4 , in circular motion 5,6,7 , carried by a student 8 and in free fall 9,10 as well as the effect due to the motion of the receiver 11 have been studied. Demonstrations of Doppler effects from real cars have also been performed 12,13 .…”

Measuring the acceleration due to gravity using an IR transceiver

“…Of the many simple techniques employed to measure acceleration due to gravity in standard physics books, the utility of the pendulum period of oscillation, as well as the time of fall of an object as a function of height, are the most commonly used methods [14,15]. While the pendulum method can yield a relatively wide range of variation in the value of g due to the effect of air resistance and other systematic errors, the lateral method can be very sensitive to imprecise measurements of times and heights of fall, consequently causing significant variation in determining the value of g. In the last few decades, many experimental techniques have been proposed to replace these two simple methods to evaluate g [16][17][18][19][20][21]. However, the application of these techniques was either deemed expensive or inaccurate and sometimes unsafe.…”

The acoustic Doppler effect applied to the study of linear motions

“…The "plus" sign indicates that the observer approaches to the source (the frequency increases), and the "minus" sign indicates that the observer moves away (the frequency decreases). There are various articles on acoustic Doppler effect experiments reported in the literature [8,9,10,11,12,13]. Different lay-outs have been used.…”

“…The theoretical curves of the measured sonogram were superposed yielding a good agreement. In reference [13] the authors measured the instantaneous Doppler-shifted frequency of a free-falling sound source. The acceleration of gravity was calculated from the slope of the frequency versus time.…”