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Here are some ideas to be considered: What was the position of the source, microphones and starter at the beginning of the experiment? To get a reasonable data the source should be already moving when passing the first microphone. Do you have a signal long enough (in time) Fourier analysis to be precise? Did you try that on more frequencies? If you don't ...

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Yes, I think so. Since we don't have the source behind our backs, we will "meet" the sound and be able to hear it. When we pass the stereo, we will be able to hear the sound of the "stereo history" (i.e. already radiated) but not any "new one" (radiated post our flyby).

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First, note that there is a slight error in your equation. In Einstein's paper (on page 16), it is the square of the amplitude that is written: $$A'^2 = A^2 \frac{\left(1 - \cos \frac{\phi v}{c}\right)^2}{1 - \frac{v^2}{c^2}}$$ So the proportionality relation is: $$A \propto f$$ Also, we should be careful with the definitions. The amplitude that is ...

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The question details contain a misconception: "due to the expansion of the universe (and thus not related to the Doppler effect)". Actually, whether or not a distant galaxy is receding from us because of expansion or some other reason, the Doppler shift will be the same. (As a matter of fact, with the exception of spatial curvature and the cosmological ...

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First off, the Doppler effect (in this case cosmological redshifting of distant galaxies) is a direct result of an expanding universe, and was used by Hubble and others to measure the expansion velocities of such galaxies (and thus the universe itself). I found a great little ditty on this topic in Matt Roots' Introduction To Cosmology: The Expanding ...

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