What’s described above isn’t quite the same as delay line memory.
Delay line memory relies on the speed of sound through a medium. You put a signal in at one end, and it propagates “slowly” to the other, where you receive the signal, and immediately replay it at the start. Creating a kind of never ending echo.
What’s described above relies on a standing wave in a tube, with sensors along the length of the tube to detect nodes and anti-nodes. Then encoding data into that by changing the signal input to change the locations of the nodes and anti-nodes.
I don’t think such a system would actually work, because your stuck using only the harmonics of your tube as possible states, and there’s gonna be a pretty limited number that you could realistically produce.
You're correct- mercury delay lines read/write in a set order and you have to wait for your address to come back around in order to access it.
Standing wave memory would mostly defeat the point of having memory, since you'd need to address every single antinode individually. You might as well just have a bunch of latches. The real point of delay lines, shift registers, or core memory is to reduce the address space: you store bits in a way that is slower but simpler to access, which means you can store more things. Mercury standing waves would not make it any easier to store bits, so there's no advantage.
Still, you could make a device like that. Only 2/3rds of the tube can store memory- the rest is a quarter-wave transformer, which basically makes the tube act as if it was open at both ends. You can construct arbitrary patterns with fourier decompositions: https://en.wikipedia.org/wiki/Periodic_summation
> Standing wave memory would mostly defeat the point of having memory
This is a common theme in sci-fi. Authors tend to know enough to make something sound plausible; but it's pretty rare for their inventions to pass the sniff test. I'd say "they're not writing patents, after all" but Salvatore Pais took that away from me:
From what I've heard this was really sensitive to any changes in environment - temperature, vibration or possibly even air pressure.
All of which were likely to change where you were about to demonstrate your new mainframe to a delegation of important people! :-) IIRC it was even named "the general syndrome" in some places.