Doppler effect from a moving source

What you are seeing: a source moving at constant velocity $v$ to the right (cyan dot) emits a circular wavefront once per source-frame period $T = 1 / f$. Each wavefront then expands at the wave speed $c$. Because the source moves between emissions, the wavefronts cluster in front of the source and stretch behind it. The coloured bar along the source axis measures the wavelength directly: a short blue $\lambda_\text{front} = (c - v)/f$ ahead and a long warm $\lambda_\text{back} = (c + v)/f$ behind. The source loops: when it leaves the right edge it re-enters from the left and the pattern continues.

Pick any angle $\theta$ from the velocity vector. A stationary observer there hears frequency $f_\text{obs} = f / (1 - (v/c) \cos\theta)$. In front ($\theta = 0$) the frequency is blue-shifted by $1 / (1 - v/c)$; behind ($\theta = \pi$) red-shifted by $1 / (1 + v/c)$; perpendicular ($\theta = \pi / 2$) it equals $f$ in the non-relativistic limit. Move the source-speed slider toward $v / c = 1$ to see the front wavefronts pile up tightly.