Beauty in motion through the lens of Doppler’s formula

Despite ample research on beauty in nature and in mathematical representations of natural phenomena, we are unaware of studies in physics and mathematics devoted to the objective beauty induced by motion, regardless of the aesthetic qualities of the moving body. We undertake this objective by focusing on the Doppler formula, which describes the shifts in wave frequencies caused by the motion of the wave's source relative to a human observer or receiver. We uncover several fascinating golden ratio, and silver ratio symmetries, in the base formula and its mathematical moments. Furthermore, we allude to existing  applications of the Doppler Effect in conjunction with the golden ratio in computer-generated music, and sonar imagedetection technology. We also propose a similar usage of golden ratio symmetries in the rapidly developing applications of Wi-Fi and smartphones to sense human motion. In addition, we point to appearances of the Doppler formula and its moments in quantum physics, and the relativity of information, and conclude by contemplating the possibility of a deeper level of physical reality.