We know that redshift and blueshift is the result of the frequency of light waves reflected or emitted by an object lengthening or shortening due to the relative velocity of the observer moving away or toward the object. This is the Doppler effect.
However, it was stated in response to a question I asked on a sister site that the Doppler effect would also result in the apparent frequency of a pulsar's pulses being longer or shorter due to the relative velocity of the star. Given that the speed of light is constant regardless of the frame of reference (a concept I have a really hard time understanding by the way), is this correct?
My thinking is that it is incorrect. Using the analogy of a launcher lobbing medicine balls at me at a fixed rate, I can "see" the rate of launch by the frequency of when I get hit. However, if the launcher is moving away from me, the velocity of the balls lobbed at me will be slower (relative to my frame of reference), and thus will hit me with less frequency. However, if the launcher were to adjust its firing speed (i.e. speed of the ball relative to itself; frequency remains constant in this analogy) so that the balls always hit me at the same speed (thereby simulating the concept of the always-fixed speed of light), the time between them would not change.
So, given the always-constant speed of light, is it correct that a pulsar's pulse rate would appear to be different at different relative velocities?