The Doppler applet is a part of the Physlets collection of Prof. W. Christian at Davidson University.

Vary the velocity using the slider and notice how the waves are compressed ahead of the source (thus shortening the wavelength detected by a stationary observer in that direction) and stretched out behind the source (thus increasing the wavelength detected by a stationary observer in that direction).

If the velocity becomes too large, the source overtakes its own waves and a v-shaped wake is produced that is called a shock wave; for sound, this is the "sonic boom" produced by an airplane breaking the sound barrier. The velocity is given in units of the speed of wave travel for the medium. The condition for the formation of a shock wave is that the velocity of the source exceed the wave travel speed in the medium. This is true in these units when v = 1, as you may verify using the applet.

The formula in the left frame is valid only for v < < c. The Doppler applet allows you to use that formula (Classical) or one that is also correct when v approaches c (Relativistic).