ultrasound

Ultrasound

$$ T_0 = \frac{v_wT_s-v_sT_s}{v_w} $$ $$ T_0=\frac{T_s(v_w-v_s)}{v_w} $$ $$ f_0=f_s\frac{v_w}{v_w-v_s} $$

Where $v_w$ is the speed of the wave (speed of sound) and $v_s$ is the speed of the wave generator.

For measuring blood in a vein (Where the moving object is not parrallel to the observer). $$ \frac{\Delta f}{f_0} = \frac{2v\cos\theta}{c} $$