From where do waves come ? To where do waves go ?

In outer space, an observer observes a star. When observer jets out gas and moves along the light path (in different uniform motions), frequency of star light changes.

However, if light speed is constant (to observer), wave length of the light path (from observer to the star) changes also (from the formula : light speed = frequency x wave length). And Number of waves changes also. Note : Wave length is reverse number of wave number.

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Allow me to explain the problem once more, please.

Problem is about red-shift (blue-shift) or Doppler effect (caused by observer's motion. not relative but observer's motion !!). If following both are right, what does happen on the light path ??
* Constancy of light speed (to observer)
* light speed = frequency x wave length

Wave length may change. Wave number may change also. Density of waves (of the light path that leads to the star ??) may be changed by observer's motion. Unimaginable !! (our understandings must be wrong !!).

Two light paths are coming from a star. These are parallel (and close to). One is coming to observer A (moving on the light path at high speed), one is coming to observer B (moving on the light path at low speed). Wave length/wave number of two lights may be the same, and light speed may not be the same (then frequency is not the same. Note : light speed = frequency x wave length), i think.