The Doppler Effect of a Sound Source Moving in a Circle

When I first heard about an experiment that illustrates the Doppler effect by twirling a buzzer around one's head,¹ I was intrigued and wondered if this experiment would work or not. In fact, it works because you usually do not place both ears exactly in the center of the circle; this would be very difficult indeed. When the source moves in a circle, the distance from the center is always constant, and there is no approaching or receding velocity at all. Holding a microphone in the same hand that holds the string that is attached to the buzzer easily shows this simple fact. No Doppler effect is observed. Although several qualitative demonstrations and experiments of the Doppler effect have been published,^1,2 only a very few quantitative experiments are found in the literature.³ Having devised a new method to quantify the Doppler effect, described in a previous article,⁴ we thought it would be a good physics and geometry exercise to calculate and measure the frequency variations when the microphone is placed on the circular path of the buzzer.