# Data transmission in ocean

What is the greatest depth where we can communicate with the submarine over the sonar system in ocean? Also, how can we calculate how much data can be transmitted using this method?

• Sound propagation in the ocean is a complex subject, since it is affected by changes in temperature, salinity, other sources of noise, currents, etc. There is no single answer to your question. Commented Oct 22, 2014 at 19:02
• Are both shift keys broken on your computer? No, they don't seem to be broken, because you can type ? and that requires a shift key. In that case, use proper English capitalization. This is mandatory on EE.SE. Commented Oct 22, 2014 at 19:02
• I'll guess all the way to the bottom. (or at least as deep as the subs can go.) Don't humpback whales communicate over hundreds of miles with sound? Commented Oct 22, 2014 at 19:59

There is no hard limit on depth. This is the same problem as radio communication, except our message is not traveling as waves in the electromagnetic field, but instead as pressure waves.

The Shannon-Hartley theorem relates channel capacity $C$, bandwidth $B$, signal $S$ and noise $N$ powers in a channel subject to Gaussian noise. The theorem is:

￼￼$$C = B \log_2\left(1+\frac{S}{N}\right)$$

This doesn't directly answer the question of "how deep", but realizing that acoustic power, just as electromagnetic power, decreases with the square of distance according to the inverse square law, it's not a big conceptual jump to see that the signal power is a function of the power of the transmitter and the distance between the transmitter and the receiver. If you want to communicate over a greater distance you could:

• reduce the noise,
• increase the transmitter power, or
• reduce the channel capacity.