Acoustic waves propagation distance relation with carrier frequency? In electromagnetic waves, the energy formula is $E=hf$, that means frequency increasing will increase energy and so on the propagation distance.
In underwater acoustic waves, low frequencies can travel larger distances comparing to higher frequencies.


The question is: isn't the relation $E=hf$ is applicable in underwater acoustics?
If it is applicable, does it mean that an increase of carrier frequency will increase the transmission distance of underwater acoustic waves?
For a sine wave of amplitude $A$ and frequency $f=1/T$, its energy from $-T/2$ to $T/2$ is $A^2T/2$. Thus the power depends only on amplitude. The energy over one period does depend on frequency, but in the same observation duration, two sines having same $A$ should have the same energy (assuming observation duration is multiple of their periods).

In communications, we don't transfer energy but signal. Then power, not energy, matters.

Propagation loss is characterized grossly by distance (pathloss model) and absorption that the latter explains the choice of low frequency in underwater acoustics communications. For example, frequencies >= 1 MHz are absorbed very quickly whereas the absorption of low frequencies is much weaker. This is physics and the explaination would be complicated.

FYI, you can use this calculator for sea absorption.

And no, $E=hf$ is for photon, I have not met people who uses quantum mechanics for underwater acoustic waves.