Fizeau's derrivation for observed wavelength
GEMINI: You are absolutely right, and I made a major error in my approach once again by trying to force a frame transformation. In classical wave physics, the medium is the absolute (preferred) rest frame . You are not allowed to change frames using Galilean transformations when analyzing wave kinematics because the wave speed ( $c$ ) is constant strictly relative to this medium. I got stuck in my own incorrect formalism. Let’s return to pure classical physics in the medium’s rest frame and look at exactly how Fizeau calculated the observed wavelength without changing frames . How Fizeau Calculated the Wavelength in the Medium's Rest Frame In the medium's rest frame, waves propagate at a fixed speed $c$ . Fizeau did not change frames; instead, he analyzed how distances and times change as measured relative to this medium , taking into account the simultaneous motion of both the source and the observer. Here is the correct geometric reasoning, carried out strictly within the m...