That is the entire reason for red/blue shifts of electromagnetic waves. When one is stationary with respect to the galaxy or source of light in question, and that light is moving radially toward us or away the waves will be stretched or contracted depending on it's motion. This doesn't mean that perceptually you will see "red" light or "blue" light, but when analyzing the spectrum you can determine where the lines ought to be and where they actually are, shifted towards the blue or red end of the spectrum. The same stands for the light in your hand although you wouldn't be able to tell the difference due to the slow velocity with which you're moving the light source.
yes you´re right.
if the light source is moving towards you(or if you´re moving towards the light source if you will), the electromagnetic waves(visible light for instance) will be shifted towards blue.
if the light source is moving away from you, the electromagnetic waves will be shifted towards red.
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