At 90°, cosθ = 0, so f_D = 0. The machine sees no Doppler shift and reports zero velocity — regardless of how fast blood is flowing. This is not a machine error; it's geometry. Always keep your angle between 30° and 60°.
Christian Doppler described the frequency shift of light from stars in 1842. Medical ultrasound application came in the 1950s–60s — over a century later. The math had been sitting in physics textbooks, waiting for transducer technology to make it clinically useful.
Color Doppler assigns red to flow toward the probe and blue to flow away — by convention. It doesn't show arteries as red and veins as blue; it shows flow direction relative to the probe. Rotate the probe and the colors flip.
Doppler shifts for blood flow at 7.5 MHz fall between roughly 200 Hz and 15 kHz — squarely in the audible range. The audio output of a Doppler machine is not a representation; it literally IS the frequency shift, converted to sound.