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It is true in principle. But the speed of sound is different, depending on the material. For that string we can assume it to be roughly 10 times faster than in the air.
~ 1 hour then.
Wouldn't the motion of the string move at the speed of the pull!? Assuming no compression.
Compression and expansion is real. The first part of the string moves with your hand, at the same speed as your hand moves. But then it takes some time until further parts of the string - or the final part of the string - even start with their motion. Ok? And here we were talking about how fast this "beginning of the motion" travels forward through the string. That's the speed of sound.
Okay, but what if there is no compression or expansion? What if it's a rigid string already stretched out just enough to be expanded completely but not enough to move the bell? Or maybe a thin wire of the same weight?
That means, the speed of sound is infinite in your material. It doesn't happen in this world.
Physics. The force you place on that string will effect the far end only at a rate no sooner than the speed of sound thru said medium.
The speed of sound in metal is about 17000 feet per second. Of materials on earth it has some of the fastest rates of transfer. But if you had a metal rod 17000 feet long and pushed one end a foot, the other end wouldn't move a foot till a second later. It will compress.
Interestingly a neutron star has material that is so densely compacted that the speed of sound thru that material is approaching that of the speed of light.