physics//wave//Doppler effect
The Doppler effect is the change in the frequency of a wave when its source, its receiver or a reflector moves along the line between them, and it is how radar guns, weather radar and Doppler ultrasound measure speed instead of distance. A siren rises in pitch as it approaches and falls as it leaves; the instrument version sends a known frequency and measures how far the echo has drifted from it.
The Doppler effect is the change in the frequency of a wave when its source, its receiver or a reflector moves along the line between them, and it is how radar guns, weather radar and Doppler ultrasound measure speed instead of distance. A siren rises in pitch as it approaches and falls as it leaves; the instrument version sends a known frequency and measures how far the echo has drifted from it.
For a wave travelling in a medium at speed ccc, with source and receiver moving along the line that joins them, the received frequency is
f=c±vrc∓vs f0,f = \frac{c \pm v_r}{c \mp v_s}\, f_0 ,f=c∓vsc±vrf0,
with the upper signs when they approach. An echo instrument gets the shift twice (the reflector receives the moving wave and re-emits it while moving), so for a reflector moving at vvv at an angle θ\thetaθ to the beam, and vvv much smaller than ccc, the shift is fd=2f0vcosθ/cf_d = 2 f_0 v \cos\theta / cfd=2f0vcosθ/c.
The shift reads only the motion along the beam.
At 90 degrees cosθ=0\cos\theta = 0cosθ=0 and a fast flow shows no Doppler at all, so every Doppler measurement is a measurement of speed times an angle someone has to know.
The numbers land where they are easy to measure. A police radar at 24.15 GHz watching a car at 30 m/s sees a shift of about 4.83 kHz; a 5 MHz ultrasound beam on blood moving at 0.5 m/s gives about 3.2 kHz, inside human hearing, which is why Doppler machines can play the flow as sound.
The sign gives the direction, toward or away, and colour Doppler paints it on the image, red and blue by convention, over the grey-scale picture.
Many medical systems measure the phase change between successive pulses rather than the frequency of one echo; the physics is the same, the signal processing differs.
Separating moving blood from still tissue by its Doppler signature is the basis of imaging blood flow in small vessels, which ultrasound uses to map brain activity.