  We explain simple laboratory experiments for making quantitative measurements
of the Doppler effect from sources with acceleration. We analyze the spectra
and clarify the conditions for the Doppler effect to be experimentally
measurable, which turn out to be non-trivial when acceleration is involved. The
experiments use sources with gravitational acceleration, in free fall and in
motion as a pendulum, so that the results can be checked against fundamental
physics principles. The experiments can be easily set up from ``off the shelf''
components only. The experiments are suitable for a wide range of students,
including undergraduates not majoring in science or engineering.
