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Most of the content that we download or get from media is 24fps. Which can not play smoothly on 60Hz/50Hz monitor as 24 frame can not directly sync with 50/60Hz monitor.

Now my question is it possible to directly play 24fps video smoothly on 50Hz monitor by increasing the speed of video by 1.05x by which it will become 25fps video which can directly sync to 50hz screen. If I'm technically correct what is the best way to accomplished this.

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I believe you are technically correct but that in practice it would not be done in that manner.

In other words, if you simply increase the playback speed there will be visual and/or audio artifacts from the speed change.

What you would want to do is use software that would adjust the frames directly, like by dropping every 20th frame.

While I said you are technically correct, I believe your premise is slightly misguided. Have you noticed any artifacts from playing video on monitors with different frame refresh rates?

Your brain is an amazing tool and can fill in gaps so dropping a few frames wouldn't usually be noticed. But your brain has a top speed that it can process things like you describe.

24 fps is selected for cinema, as I am sure you know. Video these days is usually recorded at much higher rates.

But think for a minute about why they chose 24 in the first place. it is because if the frame rate drops below about 18 or so you can actually see the jumps between frames. This is partly why interlacing was introduced, so a 30 fps transmission is half-drawn in between frames and the interlacing lets your brain melt one frame into another.

That's why stills from those kinds of programming - like old Betty Boop cartoons - look funny. It is hard to capture a single frame unless your software is aware of the format. Simple screen captures are not.

The point of mentioning the 18 fps thing is that above that most people can't see any syncing problems like you describe.

I would suggest you put this kind of question into Google in various ways and find others who have asked similar questions.

Have a great day.

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