We are attempting to penetrate 1m of water featuring dissolved ions ( assume salinity of sea water) using radio waves. Aside for using wavelengths of very low frequency radio or below, what would be the best frequency for achieving this task?
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Underwater radio transmission at VLF frequencies has been used for many years by the US Navy to send signals to submerged submarines. Wikipedia has a good article on this which will answer all your questions. Here is a very brief summary:
VLF (10 to 30kHz) signals can penetrate ~tens of meters into seawater, but the wavelengths involved are in the range of 300 to 10 kilometers (!!!). Efficient radiation of RF power at those frequencies requires a vertical 1/4-wavelength antenna which is impossibly tall. For this reason, all practical VLF antennas are classed as electrically short which means extremely ineffective- which requires them to be driven with huge amounts of transmitter power (~megawatts) in order to produce useful RF signal strengths.
Note that 540 kilohertz is very close to the commercial AM broadcast band and to get seawater penetration will still require many megawatts of transmitter power and an antenna hundreds of feet tall.
Note also that you can shorten the required antenna by using the design rules for electrically short antennas but the transmitted radiation effectiveness (also called the radiation resistance) is extremely low so you will inevitably run right up against the severe limitations of short antennas.
The ARRL Antenna Book (used by ham radio operators) contains most of the design equations for VLF antennas.
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