Could submarine SONAR kill a diver? Could a diver swimming next to a submarine be killed or seriously injured by its SONAR?
What physical aspect of SONAR affects the human body in a potential harmful way?
 A: Potentially yes it could. 

There are no noise-cancelling headphones to stop the U.S. Navy's 235-decibel pressure waves of unbearable pinging and metallic shrieking. At 200 Db, the vibrations can rupture your lungs, and above 210 Db, the lethal noise can bore straight through your brain until it hemorrhages that delicate tissue. If you're not deaf after this devastating sonar blast, you're dead.

I found this from an article about killing with sound:
Killing With Sound
A: Raphael,
Active SONAR emits pressure waves that bounce off of things in the water; the timing of the pressure wave bounced back is used to measure distance and develop images of what is underwater.  Given that the energy in the pressure wave dissipates at a rate defined by the inverse of the square of the distance traveled (1/r^2), it obviously takes a tremendous amount of energy output to receive a measurable bounce-back.
Think of it this way: A pressure wave from active SONAR acts the same as a pressure wave from an exploding mine, torpedo or depth charge.  Given that the pressure wave from a mine, torpedo or depth charge can rupture the steel hull of a submarine, how much damage do you think a pressure wave could do to living tissue?
This is why military submarines will turn off any active SONAR systems when divers are in the water, to avoid injury or death that could occur if that much energy were put into the water with a diver nearby.
This is from my personal experience as a submarine officer.
A: The effects are twofold. The first is similar to the damage caused by an explosion. The shock wave will travel through tissue without too much harm until there is a density discontinuity, for example flesh to air in the lungs. You then get a "Newtons Cradle" effect which causes mechanical damage to the lungs.
The second possible cause of damage is tissue rupture caused by cavitation ie tissue is literally ripped by the back and forth effect of the sound. This is more of a concern for continuous sonic feed.
So yes - it could injure or kill.
