Infra-sound Carrying Quality

Question

I was told that infra-sound has a larger range than audible sound. That is the reason why we hear distant thunders as a deep rumble while closer thunders have an audible "crack" that explodes with high frequency. The thunder is audible in the lower frequencies at longer distances even though most of the energy of the lightning bolt that started the thunder was dumped into the higher frequency modes.

Suppose I want to create a broadcasting device that uses infra-sound to send messages across long distances. I don't have gigantically powerful infra-sound radiators to produce anything even close to a thunder so the range will likely not be many kilometers. And I would like to transmit something more ordered. Music... Or voice, if at all possible.

But this is the thing, I don't know what is possible. A friend of mine told me that this was something called the "carrying quality" of the sound and he also said that my fictional telecommunications device should also consider the possibility of using infra-sound going through the ground rather than the air, since rock is less elastic and the sound wave propagating through it not only would be faster but would experience less dissipation. He said elephants could communicate long distances like that, which I thought was amazing.

I asked him about how that all fits together, carrying quality, elasticity of the medium, sound speed, energy imparted in the signal and the mode of production. He did not manage to give me a straight answer but he said that if I wanted to generate the ground waves, I would need a giant apparatus to stomp the floor in a systematic manner. Might be harder to transmit voice... But what about air? Can I create a "megaphone" for infra-sound voice generation?

So now I'm asking here where I know there are a bunch of physics wizards:

How are the carrying qualities of infra-sound tied to the energy of the signal, the dissipation of the signal along its path, the elasticity of the medium and the range of the wave?

Is there a formula for quantifying these things?

P.S. I know this would be an extra question, but can I transmit voice via infra-sound using a giant megaphone? I'm very curious about that one.

Answer 1

There are several fundamental but not really physical limits you have to take into account when such estimate is to be made.

(1) The first is Shannon's Channel Capacity Theorem (CCT), see, Shannon that expresses that there is an upper limit for the maximum rate of information transfer across a channel that is disturbed by noise. Shannon's result refers to an abstract channel and is independent of the type of physical channel being used as long as you can identify on its operating SNR and bandwidth. Note that Shannon's CCT limits the *maximum rate *of information transfer not the maximum amount of information while achieving arbitrarily small error rate. This is why we could still receive/decode the Pioneer spacecraft trillions of miles away, but the information rate was very very low.

(2) The information rate of your information source. This will tell you how many bits/sec your channel needs to support and will be applied in Shannon's CCT. This is the source encoding problem, and, again, is not a physical limit on a real channel but rather a requirement without which no communication can exist.

(3) The amount of delay the user is willing to live with. To apply (1) + (2) and to exploit the maximum available information rate the channel allows, you will have to spend more and more time and thus suffer longer and longer delay to deliver the information (not computer clock cycles but real transport delay time). This is the problem of modulation/encoding the source and demodulation/decoding of the received noisy signal.

(4) Given the required information source rate what is the signal type to be used in the channel. This is the physical channel problem and its limits are in the available technology, regulatory issues, costs, etc. In your question you are suggesting using the lower end of the acoustic spectrum, say below 100Hz. But music, human speech, etc. have natural bandwidth (amplitude fluctuation rate) 3kHz to 15kHz . This means that you will have to slow down your rate of communications and then spend an enormous amount of time just to encode your signal even before you get on the channel. But if you can get it on the acoustic channel with sufficient fidelity equipped with appropriate encoding (sufficiently low rate) you will be able to receive the signal almost err-free at the same rate, there is no physical limitation. (Elephants stomping the ground once per second is low rate communication in this sense.)