Here is an interesting page on what is known as the "Seeburg" quadraphonic "decoder" system, used on a certain series of old Seeburg jukeboxes (from the 1970's, I believe):http://home.pacbell.net/fmillera/quad_decoder.htm
If you scroll to the bottom area, you will see how the speakers were wired up to allow panning left-to-right, front-to-back, using potentiometers connected between the speaker pairs to vary the volume.
You could use a similar system, and change the volume mechanically by coupling servos to the potentiometers, then changing the servo positions with the Arduino based on the PING sensor readings, but this may or may not be fast enough or what you want.
The better approach might be to do this at "line level" (instead of "speaker level"), and hook the line level signals from your sound source though digital potentiometers (connected in the same manner as shown in that diagram), and control these directly with the Arduino (based on the PING sensor readings). This device would then sit between the outputs of your line-level sound source(s), and the line-level inputs into your amplifier(s) driving the speakers.
Alternatively, you could use four digital potentiometers, one between each line-level source and amplifier, and then do the mixing of levels and such in software (you would end up with close to the same arrangement - although you would have slightly better control options since the speaker channel levels wouldn't be coupled).
Hope this helps!
Hmm - looking at that Seeburg setup, I now see that it is more of a Haffler mod than anything (not quite the same as true quadraphonic sound); still, look into usage of digital potentiometers, and placing these at line-level between your sources and the amps/speakers...[/edit]