Why is fourier analysis used in doppler effect?

Question

I am a high school student that carried out the experiment on the Doppler effect to therefore analyze the graph but after doing some research, I saw one of the articles saying “ Fourier analysis is a mathematical tool that allows us to extract information about the frequency spectrum of any signal.” I don’t understand, could this be used in my analysis and what does it actually mean?

This experiment was carried out under normal conditions in other words at home and the procedure of this experiment is quite simple where I would be rotating a sound source producing constant frequency in a circular and a smartphone would be recording the data using the app. The results I got shows sharp peaks and frequency ranging from 425 when away from sound source and 441 when in-front of sound source with of course ups and downs due to errors of measurements. The idea is that I am creating a report on how math is used in a real life scenario and so I will be analyzing the graph I got by using different mathematical analysis techniques and therefore this is where I am stuck and looking for what math can be applied to my modeling change in frequency report.

(For my experiment I got sharp peaks of minima and maxima incase you wanted to know what my results were like because unfortunately I have no clue=e how to post my results here)

I was also told by one of the professors from math stack exchange that it would be a good idea to ask this question here

Reference: http://www2.york.psu.edu/~kxt7/Labs/Doncheski/doppler/lab01.pdf

Answer 1

The fourier transform of a signal (like sound) will show you the sound in the frequency domain. In other words, the independent variable, or x axis, will be in terms of frequency (such as hertz or radians per second), and the y axis will show the magnitude of those frequencies.

One reason that the fourier transform is useful is that it will show what frequencies are present in a signal and in what quantities. When used in the experiment you described (if I understand it correctly), you could help demonstrate the doppler effect by showing that the sound source is outputting a tone of a constant pitch, and in the recording of the sound source moving in the circular pattern, the fourier transform of the recording will show that the frequency is not constant, and appears in significant quantities in the sound. If you record the sound as the source moves in a circle, then the fourier transform of the sound should appear to be high in a range close to the pitch that the source is outputting.

A tool I frequently use for computing the fourier transform of an audio file is matlab. I am sure there are many tools online to help you compute this as well if you do not have access to matlab.