Doppler Shift Formula

The Doppler shift is given by

$$\omega_l = \omega_s \frac{1+\frac{v_{ls}}{c}}{1-\frac{v_{sl}}{c}}$$

where

• $\omega_s =$ radian frequency emitted by the source at rest
• $\omega_l =$ frequency received by the listener
• $v_{ls}=$ speed of the listener
  relative to the propagation medium
  in the direction of the source
• $v_{sl}=$ speed of the source
  relative to the propagation medium
  in the direction of the listener
• $c =$ sound speed

Note that all quantities in this formula are scalars (not vectors)