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I thought the UNIVAC used a form of wire memory, https://en.wikipedia.org/wiki/Plated_wire_memory So calling it acoustic memory does seem a stretch for me, but then any electrical pulse plugged into a speaker would have an acoustic sound.
Univac I used mercury delay lines:

https://en.wikipedia.org/wiki/UNIVAC_I#Main_memory_details

They're called acoustic because a transducer much like what you'd use for a high frequency piezo speaker sitting on one end would inject pulses into the fluid mercury and the pulses would be detected on the other end of the delay line using a second transducer. You could do the exact same thing with a speaker, a microphone and air as your working fluid.

Later UNIVACs such as the 9000 series used plated wire memory (as described in http://www.technikum29.de/en/devices/plated-wire-storage). However, while plated wire memory uses magnetization (already similar to the hard disks we still use today), delay line memory exploits the finiteness of signal traveling times which is a totally different concept.

Back in these days, storing data was really a challenge. We are talking about working memory here, by the way. For persistent storage, all kind of punched cards and tapes were ubiquitous and magnetic tapes were in fashion. Still today, for cheap long term archival, magnetic tapes are unbeaten!

Mercury delay lines were a form of memory that predates and is distinct from plated wire memory. Plated wire memory is magnet memory, like core memory, but with permalloy coated wires rather than little permalloy donuts like the elements of core memory.

Delay line memory uses a transducer that puts vibrations into a medium in a tube (mercury) that travel the length of the tube at the speed of sound through that medium (1450 m/s) a transducer at the other end picks up the vibrations and decodes them back into bits. While the signals are being sent down the tube they are "in memory". By sending the signals back to the beginning of the tube a set of bits can be kept recycling indefinitely (120 bits per delay line in the UNIVAC I).

The UNIVAC I only had 1000 thirty-five bit words in its memory. These were store in a set of these mercury delay lines.

In my first digital design lab course at MIT there were a few old delay line memories kicking around which I briefly considered using for a project. I ended up needing only 5 shift registers of around 6 bits each so I just used flip flops to build them for the nim-playing computer I built.

1100/10 (maybe called 1110?) used plated wire. Other Univac models used various memory technologies, going with the technology of the times. Engineering Research Associates built a machine with Mercury acoustic delay lines, and a 1 bit serial ALU. ERA and Echart-Mauchly merged to form Univac, I believe. One of my profs worked on the ERA machine with delay line memory.

Later he got into magnetic storage, and his PhD students went on to do a lot of important work in core and later magnetic bubble memory.

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There is another kind of acoustic delay line that was used in late 50's - early 60's that used nickel strips and took advantage of magnetostrictive property of Ni. I'm calling it acoustic because the memory was in the form of a compression wave propagated from driving magnet to sensing coil, then regenerated. Elliott Brother's 803 series computers used these for the CPU registers.