The question of how loud sounds are in water has bugged me for time now, simply because it is often repeated, just like in this thread, that "sounds are louder in the water than in the air." I had a hard time believing that sounds actually get louder, I mean, there are no amplifiers in the water, so in order to look deeper into the question of how sound behaves differently in water than in air, I read the article "Viscosity Effects in Sound Waves of Finitie Amplitude" by M.J. Lighthill in the book
Surveys in Mechanics published by Cambrige Univeristy Press
In Lighthill's article, there was a formula given for the diffusivity of sound, that is, the rate at which the sound will be muffled and spread out. This diffusion rate can be thought of as the rate at which the sound wave goes from peaks and valleys to a flat line.
diff of sound = kinematic viscosity*( (4/3) + (ratio of bulk to shear viscosity) + (ratio of heat capacities - 1)/(Prandtl number) )
d = v*( (4/3) + r + (g-1)/s )
d = diffusivity of sound, in m^2/s
v = the fluid's momenum diffusivity
r = ratio of bulk (or dilational) visocity to the shear vicosity of the fluid
g = ratio of the constant pressure heat capacity to the constant volume heat capacity
s = Prandtl number, the ratio of the fluid's momentum diffusivity to the fluid's heat diffusivity. Basically, s compares which diffusies faster in the medium, heat or momentum.
Anyway, I calculated these numbers for both air and water:
d_air = 5.8 * 10^-5 m^2/s
d_water = 4.8 * 10^-6 m^2/s
So you see that the sound diffusivity of air is more than 10 times that of water.
In other words, sound gets spread out and dies out more quickly in air than it does in water.
It seems to me, that sound is no louder in water than it is air, its waves remain sharper for a much longer time in water, therefore the sound does not die out nearly as quickly.
For example, someone yells at you from the end of an (American) football field, 100 yards away. If you were both underwater, it would be the same as them yelling from 10 yards away in air. Not because the person yelled any louder, but because the water keeps the sounds waves intact for a much longer time. (This is a very simple example that uses only the difference in diffusivities, there is undoubedly a difference in wavespeeds in air and water also, but 100 yards is a small enough distance and the wavespeeds so fast in both media that the difference in wavespeed error is probably small to negligible.)
Then, there is also the question of the air-water interface. Water is almost 1000 times as dense as air, and from
http/www.du.edu/~jcalvert/waves/soundwav.htm "Waves from the air do not penetrate into water, and sound waves in water do not penetrate into the air. The two media are acoustically separate. This may be of interest to anglers, who can feel free to talk while they fish. They should beware of casting moving shadows on the water, however."
Basically, the density difference means that only a tiny portion of sounds from the air will be heard in the water.
So, in conclusion, sounds in water are not louder, but do not diffuse and become muffled as quickly as they do in air.