We will focus on sound waves in describing the Doppler effect, but it works for other waves too.

Consider a stationary source of sound broadcasting a single frequency sound wave. You are the observer of the sound wave, and you are also stationary. The usual relationship between frequency, speed, and wavelength is:

f = v/λ

v represents the speed of sound through the medium.

Let's say you, the observer, now move toward the source with velocity v_O. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed:

v^/ = v + v_O

The frequency of the waves you detect is higher, and is given by:

f^/ = v^//λ = (v + v_O) /λ

If you moved away from the source the observed frequency is lower. In general the observed frequency when the observer moves is:

f^/ = (v +/- v_O) /λ = (v +/- v_O)* f/v = f * (v +/- v_O)/v

Use the first sign (+) when the observer moves toward the source and the second sign (-) when the observer moves away.