I am trying to penetrate about 8 ft of seawater with a radio wave. What wavelengths will work? I understand that low wavelengths penetrate seawater the best, but I am looking for a frequency that does not require a large emitter (it should not be larger than an average table). Does anyone know of one?
You're largely out of luck. Seawater is simply too good of a conductor to pass radio waves — instead it reflects them like a mirror off of its surface. According to EM GeoSci the skin depth of saltwater is 0.277m (0.9 feet) at 1MHz, and skin depth is inversely proportional to the square root of frequency. So in order for 1/e (about 37%) of a signal to reach a depth of 2.4 meters (8 feet), the signal should have a frequency below about 13kHz. If you're okay with only 1% of the signal making it to that depth (20dB loss compared to a receiver at the surface) then the signal still needs to be below 275kHz. While antennas for these frequencies exist, they are very large, very inefficient, or both. There are no "windows" of higher frequencies that penetrate seawater more effectively than this.