Submarine communications and RF skin depth

[Guineafowl]

TL;DR Summary

How does visible light penetrate seawater, when even a 1 MHz signal struggles? The question comes from studying how submarines communicate.

In conductive media like seawater, EM waves experience attenuation related to their frequency. The skin depth formula calculates the depth at which $e^{-1}$ attenuation is reached. The skin depth is inversely proportional to frequency.

In practical terms, only extremely low frequencies (eg 80 Hz) are able to penetrate significant distances, and the range of even a 1 MHz signal would be a metre or two.

So how is it that blue light, an EM wave around $10^{14}$ Hz is feasible for submarine comms, or to put it another way, given the above, why am I able to see things when swimming in the sea?

 

[.Scott]

Generally, when submarines want to communicate , they want to communicate with something miles away - and they do it by sticking something above the water (an antenna on their sail or a tethered buoy) and using radio communications.

A discussion of how water absorbs EM is available in wikipedia.

You (@Guineafowl ) have not cited your source for the equations you are using. But I believe that if you check that source, they only deal with the electrical conductivity of the liquid and apply only to radio frequencies that are not assisted by the actual chemistry of the liquid.

 

[Guineafowl]

Apparently, fresh water RF comms are feasible, eg:
http://eprints.gla.ac.uk/194214/7/194214.pdf

Regarding seawater, an example formula is here (page 317):
https://www.researchgate.net/profil...dubG9hZCIsInByZXZpb3VzUGFnZSI6Il9kaXJlY3QifX0

$$\partial = \sqrt{\frac{2}{\mu_0 \sigma \omega}}$$
Where:
$\partial$ = skin depth
$\mu_0$ = permeability of free space
$\sigma$ = conductivity
$\omega$ = angular frequency

Some examples are given by this RF engineer in a very interesting video:


Reproduced here.

Frequency:	Skin depth in seawater (m):
1 GHz	0.015
1 MHz	0.280
1 kHz	8.800
1 Hz	280.0

With that trend, a $10^{14}$ Hz blue light wave should have no chance, so there’s something I’m missing. If I’ve read your last sentence correctly, @.Scott , are you saying that at visible light frequencies, a different effect comes into play that overcomes the attenuation?

 

[renormalize]

With that trend, a $10^{14}$ Hz blue light wave should have no chance, so there’s something I’m missing. If I’ve read your last sentence correctly, @.Scott , are you saying that at visible light frequencies, a different effect comes into play that overcomes the attenuation?

The EM absorption of water varies strongly with frequency. There is a passband at visible frequencies (which is no doubt why animals, including humans, evolved eyes to detect this band). From J.D. Jackson, Classical Electrodynamics, 2nd ed.:

 

[Baluncore]

80 Hz can be used to call a submarine, to listen at higher frequencies from closer to the surface.

Space and airborne radar is used to measure the thickness of sea ice and icecaps. Ice is more resistive than seawater, and has a low Er = 3.15 compared to liquid water, Er = 80. That can make icebergs difficult to see with radar.

Where a submarine rests on the bottom, near a port on a river, fresh water flows out over the salt water. The submarine can rise to be at a stable neutral buoyancy, in the salt-fresh water boundary, then communicate through the fresh water.

 

[DaveE]

The skin depth is inversely proportional to frequency.

Only in simple conductors with constant resistivity.

In practical terms, only extremely low frequencies (eg 80 Hz) are able to penetrate significant distances, and the range of even a 1 MHz signal would be a metre or two.

Which is soooo far away from blue light as to be irrelevant.

Don't confuse what you read in an EM textbook with chemistry. Metals are special because of the (relatively) free conduction band electrons; that's not like sea water.

The term spectroscopy comes to mind...

 

[Guineafowl]

The EM absorption of water varies strongly with with frequency. There is a passband at visible frequencies (which is no doubt why animals, including humans, evolved eyes to detect this band). From J.D. Jackson, Classical Electrodynamics, 2nd ed.:

View attachment 343405

This seems to explain it - thanks. Another example of how the fascinating behaviour of water has enabled and shaped life.