If you have a lake nearby - this could be an interesting way to visualize it differently.
Toss two stones in the lake at the same time in different areas - but not too far apart. When the waves hit each other, their combination causes the amplitude of the wave to increase, decrease, or stay the same. This will not be consistent everywhere in the pond - some places the waves will increase each other, other places they will decrease each other. The one interesting thing is that once the waves pass through each other, they continue on along as if nothing at all happened. "Destructive interference" only exists in certain area's - it's actually pretty cool to look at. If you can get large bands in the water you will see that at some point their interaction will make no wave at all, in others it will create a big wave (relative to the size of the wave without any interaction).
One thing to remember is that the waves created in the example above typically only travel in two directions. Since sound waves travel through air, and air exists in all 3 dimensions - the resulting interactions are much more difficult to visualize - however for some reason not much time is spent visualizing the vertical domain.
Some will say it doesn't matter but I disagree - it matters just as much, it's just that most of the time we can't do much about it - just food for thought.