What is the behavior when a wave pass through another wave and what type of behavior?

Answer 1

No matter the type of wave (Transverse or Longitudinal), all waves follow the Principle of Superposition. This principle is described very aptly by its name. For example, (In an ideal world) if you took a long jump rope and tied one end down, you could move the jump rope up and down once and watch a wave go to the wall, and then come back towards you, and attempt to whip the rope out of your hands. Now lets say you move your hand up and then down, sending a full sinusoidal wave down the rope. When the first wave hits the wall and is reflected back towards you, for a moment, the rope will be completely flat (at the wall).

This is because the waves superimpose over each other. The wave going up is put over the wave going down, momentarily canceling the waves out.

The most surprising part is when the waves suddenly appear from nowhere, and the wave that you initially created comes right back towards you. This demonstrates the other side of the Principle of Superposition. While waves can interact with each other to either double in size or cancel out, after the point where they interact, they separate, ideally completely unaffected by the other wave.

This Principle of Superposition affects ALL waves, including vibrations and sound.

If this is applied to earthquakes, it is curious to note that you can't fight an earthquake with an earthquake without creating an earthquake 180o out of phase at the exact epicenter of the earthquake, which is quite improbable. The worse that could happen would be that the earthquake created would become in-phase with the first earthquake, doubling the strength of the first earthquake.

All of this is ideal, which means I discount acceleration due to gravity, friction, air resistance, and I assume a constant tension of the jump rope in question.