I am studying Doppler sonography. I do understand doppler's formula: $$ f=f_{0}\frac{v}{v-u}, $$ where $f_{0}$ is emitted frequency, f is received frequency, v is speed of the ultrasound puls and u is speed of blood from which is the ultrasound puls bouncing back. But I am struggling with how to get from above formula to this: $$ \Delta f = f-f_{0}=2f_{0}u. $$ Can anyone one give me hint? Thank you.

Image I am working with

New contributor
TTeenyTiny is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
  • $\begingroup$ That does not look right. $f-f_0 = f_{0}\frac{v}{v-u} - f_0 = f_{0}\frac{u}{v-u}$ is not equal to $2 f_0 u$. $\endgroup$
    – Martin R
    Jun 23 at 7:46
  • $\begingroup$ Then I misinterpreted the image I added to my question probably. $\endgroup$
    – TTeenyTiny
    Jun 23 at 8:11
  • $\begingroup$ It looks like the image is trying to sat $\Delta F=2F_Tv/c$. $\endgroup$
    – J.G.
    Jun 23 at 8:15
  • $\begingroup$ Ok, this makes more sense.. but still is this formula directly derived from $$ f=f_{0}\frac{v}{v-u}? $$ $\endgroup$
    – TTeenyTiny
    Jun 23 at 8:26


Your Answer

TTeenyTiny is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.