Here's a better approach:
where p is sound pressure (N/m^2), ρ is medium density, c is speed of sound in medium and ξ is particle displacement. I suspect particle displacement as a lot to do with the strength of the initial sound. So lets plug in some numbers while keeping ξ = 1; ω = 314 rad/s or 50 hertz; ρ(air) = 1; ρ(water) = 800; c(air) = 331; c(water) = 1450.
In air,
p = (1)(331)(314)(1) = 103934 N/m^2
In water,
p = (800)(1450)(314)(1) = 364240000 N/m^2
In water, the sound pressure exerted (force per units squared) will be about 3500 times greater than in the air. Of course it will take a lot more energy to create this sound in the water than in the air...
Now lets look at the pressure/distance relationship which is actually 1/r. Since it's simply an inverse relationship, the pain (or in this case, death) threshold will be 3500 times further away in the water than in the air.
Someone please check my math and my assumptions. I am not an acousitcal engineer.
