Paul wrote:If we were looking at a transverse wave travelling up the page, I should be able to go from 2 to 1. On a floor say, that wave would be pushing upwards away from the rod tip and allow us to do that. But that doesn’t happen. What actually happens is that the line stays level with the rod tip and ends up in a mess. There is no upwards wave propagation.
I need to assume when you say "On a floor say, that wave would be pushing upwards
away from the rod tip and allow us to do that." you may away from you
and not upwards (i.e. vertically above the floor.)
You're not accounting for gravity when you lay your loop on the floor. Of course it's going to end up in a mess around the rod tip because you have no force acting to move it away from the rod tip. I don't know how many times I need to say it, but I'll say it again: gravity must be accounted for in this discussion!
Now, if you do actually mean "upwards" in the vertical sense, is this the scenario you're talking about:
Yes, it would end up in a mess if that was done with the rod tip on the floor. You need to allow the wave somewhere to go. Here, we can see the waves descend under the influence of gravity. In a cast, we always throw the line upwards to some extent to allow for gravity, even if we don't recognise we are doing so. That's an instinctive calculation based on our experience (e.g. when was the last time you allowed for gravity when throwing a dart at triple 20?) If you disagree with that, please find some footage of false casting with a loop above the rod tip height in which the line is not launched upwards to some extent.
This is pretty much the same thing as this video, isn't it?
Can you see the wave moving upwards through the string while it is tethered?
When the tether is released, the string falls but the wave is still moving through it. Yes, the line is falling and so is the loop.
If we make the string move upwards before we make the wave, the string does not fall as quickly and the wave does not collapse around the rod tip as it would in your scenario.