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I am learning special Relativity and I am seeing that the answer to the twin paradox involves the Doppler effect, and I am struggling to understand what is going on.

First let me explain what I know about the Doppler effect.

If an object produces waves (might it be light waves or sound waves),then if the object is moving then it will "squeeze" the waves in front of it thus resulting in a higher frequency, while the waves in the back of it will get "stretched" and this will result in a lower frequency.

This is what I know about the Doppler effect.

Yet I don't understand how it applies to the twin paradox, since the doppler effect deals with "frequency" not "speed" which is constant for any frequency even for radio waves or gamma rays.

So what effect does the Doppler effect have on the time it takes for the light to arrive to the twin?