Figure: The Doppler effect and bats

Caption: "A depiction of a bat, its ultrasound call, and the echo from an object."

As is well known, bats use echolocation to help navigate: the time delay of the echo allows them to determine distances.

Slightly less well known is that they use the Doppler effect for sound with echolocation. They emit high-frequency sound and judge relative speeds based on the frequency of the echo---and they don't need any formulae---just megayears of evolution (see Wikipedia: Echolocation: Doppler effect).