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Could sound be used in transmitting sound waves under water digitally? Could the sound then be converted by a repeater to transit by radio waves? What other ways can a signal be transmitted other than sound over long distances under water?

https://space.stackexchange.com/questions/32421/how-would-a-transmission-be-relayed-through-bottom-of-europa-ocean-to-earth

Yes, it is called acoustic communications. Here is an example of a paper that uses orthogonal frequency division multiplexing (OFDM) in an underwater acoustic channel.

EDIT:

Note that you wouldn't call it a SONAR any more because SONAR stands for SOund Navigation And Ranging, whereas this is a communication system, just like you wouldn't call your cell phone a radar.

EDIT 2:

Yes, the signal could be converted to a radio signal at a repeater. The repeater would ideally be floating in the surface and have a transducer (which is basically a microphone or array of microphones) on the underwater side to receive the sound waves. The transducer converts the sound waves into an electrical signal, which can be filtered and/or amplified, and then sent to an antenna for radio transmission. The antenna would likely need to be above water because radio waves don't propagate very far through water.

Yes, actually sound waves are better than RF signal in underwater, because of the low frequency requirement. We don't covert sound waves to radio signals. The transceiver in this case is called transducer.

EDIT: You have basically three options in underwater: RF signals, acoustic signals, and optical signals. RF signals suffer from large path loss, and the range of transmission is in meters. Optical signals suffer from scattering. Acoustic signals suffer from low propagation speed (~1500 m/s), but the transmission range is better than RF signals. Also, you don't need large antennas when transmitting low frequency acoustic signals, which is the case for RF signals. The bandwidth can be increased by using relay-assisted systems.

After a quick search, it seems that sonobuoys seem have antennas that are kept above the surface to communicate with an aircraft or a ship. This is not a wireless communication underwater. The goal of underwater acoustic systems is to exchange information "wirelessly" between node underwater, and then with a central node at the surface that uses RF signals to communication with a center for further analysis/decisions.

to be picky, RF is strongly attenuated is salt water.

Fresh water is much less attenuated. During WW2 submerged submarines could use their radios in Lake Michigan.

Very low frequency RF communications is possible in salt water. The bit rate is very low.

Fiber optic cables work well too.

Acoustics tend to be attenuated as well.

This is incredibly common in aquatic robotics. There are multiple uses for underwater acoustic communication such as data transfer, localization to a surface vessel, mission control etc.