Next time you get a pool pump, get a two-speed (e.g. Jandy Stealth 2-spd) or variable-speed (e.g. Intelliflo) pump. They cost a little more upfront ($200 for the Jandy Stealth 2-spd; ~700 for the Intelliflo,) but they are whisper quiet when they’re not on full-speed and will save you thousands over their lifespans.
How do they save you thousands? Your typical 1.5-HP pump on full speed will consume about 1500 watts, which is the same as turning on 25 60W incandescent light bulbs. You’ve got something in your backyard that is akin to leaving all of the lights in your house on while you go to work for 9-10 hours. Pool pumps are a MASSIVE consumer of electricity.
Furthermore, running a pump on full speed is terribly inefficient. All that noise and vibration that a pump makes while on full speed is wasted energy. On top of that, there’s loads of energy wasted by the high operating pressures (which just serves to make wakes in your pool — not incredibly useful) and increased resistance in the plumbing. Full-speed pumps operate at 15-40 PSI, but two-speed and variable-speed pumps operate at 0-3 PSI.
Did I mention that they’re whisper quiet? Here’s a demonstration of an Intelliflo: http://www.youtube.com/watch?v=4dIz4R-1d2k (keep watching to see it run in slow speed)
Another thing that you can do to lower the noise is to clean the basket often. When a pump has to deal with leaves clogging up its intake, it will get loud as hell — sometimes even getting more than twice as loud as it is when it is clean. The increased noise is caused by cavitation, which happens when there is either insufficient back-pressure (not a problem for pool pumps,) high pressure, low-flow conditions (not a problem for pool pumps,) and when an impeller is starved of water (a problem for pool pumps.) “Cavitation” is the term used to describe what happens when air pockets form behind the impeller blades. As the impeller blades cut through the water, they create small low-pressure pockets behind them, which can cause air to fall out of solution and can cause liquid to instantaneously become a gas (i.e. drop below “vapor pressure”,) forming air pockets, which then rapidly collapse (often at the speed of sound,) causing large amounts of energy to ripple through the water. This creates a lot of noise and is terrible for the impeller.
I’ll let someone else provide you with a passive soundproofing solution, but don’t overlook the fact that you can install it not only outside, but also inside, within the sheet rock as well.