Construstive Interference of Waves. Why don't They cancel Out?

[johnnyapplese]

Lets say there are two waves in the ocean exactly identical heading in opposite directions. It seems like logically they would cancel out since they are moving in opposite directions. Yet they don't cancel out and I can't figure out why. If two cars hit each other with same force in opposite directions they will cancel out but waves won't.

 

[pallidin]

Destructive interference does NOT stop wave propagation.
It's "destructive" only at a particular point in time, usually cyclic. The 'wave" itself continues.
That destructive interference does not destroy the wave at all, and, indeed, offers a constructive wave component afterwords or before.

 

[capandbells]

The wave fronts may be traveling in opposite directions, but the medium being displaced — in this case water in the ocean — is being displaced in the same direction by both waves.

Now, feel free to ignore this next part because I think it's not a very description of what's going on, but it may be helpful to illustrate the difference between the displacement of the medium and the velocity of the wavefront:

Imagine you had a long string of cars, say in a traffic jam on a highway. Now imagine two motorcyclists drive parallel to the cars, but in opposite directions. When the motorcyclists meet, they both fire rockets at a car so that the car is displaced twice the amount it would be displaced by one rocket. The cars are the medium, like the water in the ocean that are being displaced by the wave. The motion of the wave is represented by the motorcyclists: they're traveling in opposite directions, but that has nothing to do with the displacement of the cars.