haha, 2 science based threads in 2 days, this forums finally getting interesting! I have no problem explaining.
First thing, dont' think of it as loud/soft, it's the frequency that is changing, not the intesity. (techically it's both, but we are in a perfect world for these examples, so disregard any volume changes that would occur as it moves away or toward you)
The dopplar effect involves frequency. All the frequency of any wave is, is the distance between crests, essentially. A speaker moves back and forth creating high and low pressure areas, I think that part makes enough sense on it's own without much needed explanation? The trick is understading exactly how frequency works.
Think about it this way, if a frequency is high, it is repeating very quickly, A 20k tone reproduces itself 20,000 times in 1 second. A 10hz tone does so 10 times. Now let's add in the fact that sound waves move. If both waves move at the same speed, which wave would have more space between each crest? Well a 20k tone reproduces itself alot, meaning that the wave really wont' get very far before another one is produces following just behind it. A 10hz tone will get quite a bit further before the cone moves forward agian to produce another wave. Try and wrap your head around that, just imagine real o-scope type waves being produces and moving.
Now let's add in what happens if the object producing the wave is moving.
Ok, let's say a car is moving away from you playing a 30hz test tone. The very first speaker pulse is sent out. It heads toward you. By the time the first tone reaches your ear you the car is now further away than before right? Meaning the very next wave that is released by the speaker will be much further away than it would have been had the car not been moving. Because of this, the distance between each pulse becomes longer. Since the waves all travel at the same speed, the amount of time between each wave repeating is increased. The amount of time between the waves is exactlywhat frequency is! Think about what you learned in the first paragraph. Because the waves are further apart in reference to you, you percieve that note to be lower than 30hz. The first wave has to travel let's say, 20 meters to reach you. By the time the next wafve is sent out it needs to travel 25, then 30 then so on, since the sound isn't moving any faster toward you it takes longer to reach you, more time between each crest. wave 1...wave2.....wave3.........etc.
Consequently, if the car had been stationary and playing a 20hz tone, the time between the waves may have been just the same as the 30hz tone the moving car was playing. Ala, each wave might have been like wave1.....wave2.....wave3..... Since there is no physical differences between how the air is moving, you end up hearing the same notes, essentially. Basically for all intents and purposes that car is producing a 20hz tone relative to you, any attempts you make to measure it would show that at least.
Light works the same way, our brains interperet as color is nothing more than the changing freqency of light. Light is a wave, just like moving air particles, but they go much faster and have no mass. If a star is moving toward us, the light waves have less distance to go as each pulse is sent out, that makes them closer together. Our brains percieve higher frequencies of light to look more blue.
edit: Just realized you didnt' quite get my last explanation on subs playing 2 notes at once. I hope you can wrap your mind around this one, I'm trying to make it easy. i checked my physics books and it was purely a mathmatical explanation, no help. I guess if you have questions feel free to holla back.