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While watching videos at 1.5x or 2x the original speed I often notice a change in the speaker's voice. I am not sure if that is a change in pitch or something else, and was thinking how it could relate to Doppler effect in any way.

Both the source and observer are at rest relative to each other, only the speed of production of sound has increased which really shouldn't affect the frequency at all. Is it really a change in pitch or something like sound quality which is perceived differently by our ears?

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I don't think using the Doppler-effect is a good idea, while the outcome may appear to be the same, it 1.) can be confusing to a beginner and 2.) the Doppler effect is a very specific process that requires relevant movement between two frames of reference.

As you know, the Doppler-effect occurs when an object is moving relative to your reference frame. The thing is that when some thing is moving towards your reference frame, it is moving away from another reference frame, thus the sound frequency is simultaneously shifted up or down or not at all, depending on the reference frame. For a video, you do not have this multi-reference frame setup. You are compressing the time, not moving relative to an observer, thus this in not the Doppler effect.

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You do hear artifacts, but those are unrelated to doppler effect.

I'll get back to what you do hear, but let me first discuss what happened to analog recordings when played at a different speed.

It may be that you have never seen a tape recorder (with reel tapes), or a record player, as those are devices of the pre-digital age, so you may have to look up what those are.

A record player has two different playback speeds. One for singles, 45 rpm, and one for LP's, 33 1/3 rpm.

So for laughs you could do the following: put on an LP, and play it at 45 rpm, instead of the proper 33 1/3 rpm. Since it was all analog all the pitches were raised by that difference in play speed. Any voice, singing or speaking, sounds high and squeaky. I remember once doing that with a record of a stand up comedian. Played faster the laughter of the audience didn't sound as the laughter of adults, it sounded like children laughing.

Here is the big difference with nowadays.
Nowadays, when you adjust the computer video play setting to play a video faster the rendering algorithm does something fancy to the sound to keep it close to the original pitch. Doing that with high quality would require serious processor power, which would be a waste of energy. Instead the algorithm does it kind of quick 'n dirty; all you need is that speech is still fairly intelligible.

You hear odd distortions because the converting algorithm is doing things quick 'n dirty.

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