Lots of
possible craziness can happen with
wave superposition. If two waves
overlap, the
amplitude at any point will be the
sum of the amplitudes of the two individual waves at that point. I.e. if a
peak meets a peak, you get a bigger peak! -->
Constructive interference. If a peak meets a trough,
BOOM!, zero amplitude at that point -->
Destructive interference. (This of course assumes the two waves to have equal
period and amplitudes.
Wave mechanics explains a lot of stuff, and helps us visualise things such as atomic and molecular orbitals, and even why electrons prefer to be a certain distance from the nucleus.
One cool thing you can try on holiday or if you have access to a swimming pool, or even a water basin is: Make sure the water is still. Take your two hands and put your index fingers about 15-25 cm apart (just a reasonable distance) and pointing at the water. Dab your fingers in and out of the water simultaneously and at regular intervals (say 2-3 times a second). Make sure light is cast on the water and pay attention to the shadows of the ripples on the bottom of the pool/sink and notice how in all that turbulence, as the waves "collide" and superpose, some parts of the water are absolutely still. Simple but just cool if you can get it right.
Plenty of people will be reading this thinking, "This guy is so basic, I can solve Schrodinger's Equation for a many electron system!" whereupon I reply, "no. you can't".