Unraveling the Mystery of Wave Collisions: Same Amplitude Interaction

[Nusc]

Say we have two waves of the same amplitude are about to collide with each other.

The preceeding wave travels at a slightly higher speed before interacting with the final wave. However, instead of passing through the final wave its speed and size is transferred into the final wave where it now possesses the properties of the final initial wave. This is truly bizare. This feature only occurs for waves with the same amplitude, whereas an interaction like in figure 2, a large wave merges with a small wave for a finite amount of time with the large wave decreasing in amplitude and the small wave increasing in amplitude, then restoring its initial form after collision.

Can anyone explain to me why waves of the same amplitude behave this way?

 

[lpfr]

You are working with waves in a non-linear medium. That is, the speed of waves depends on its amplitude. When a wave catches another the speed of the sum is different of the speed for each one. What happens then depends on the dependence of speed with the amplitude and the shape of the waves. It depends on the media. The behavior you describe is just one possibility.

 

[sir-pinski]

The phenomenon of same amplitude wave interaction is a fascinating and complex concept in the world of wave dynamics. When two waves of the same amplitude collide, they undergo a process called interference, where the waves combine and interact with each other. This interaction results in the transfer of energy and properties from one wave to the other, leading to a change in the characteristics of the final wave.

To understand this process, we need to first look at the nature of waves. Waves are disturbances that travel through a medium, carrying energy from one point to another. When two waves meet, they superimpose on each other and create a resultant wave. In the case of same amplitude wave interaction, the resultant wave has a larger amplitude than either of the initial waves.

Now, let's consider the scenario of two waves with the same amplitude colliding. As you mentioned, the preceding wave travels at a slightly higher speed before interacting with the final wave. This is because waves with the same amplitude but different wavelengths have different speeds. When the waves collide, the faster wave transfers some of its energy to the slower wave, resulting in a larger amplitude for the final wave.

This transfer of energy is due to the principle of conservation of energy, which states that energy can neither be created nor destroyed, only transferred from one form to another. In this case, the energy of the faster wave is transferred to the slower wave, increasing its amplitude.

Moreover, the transfer of properties such as speed and size also occurs due to the principle of conservation of momentum. When the waves collide, they exert a force on each other, leading to the exchange of momentum and properties.

As for why this only occurs for waves with the same amplitude, it has to do with the specific conditions required for interference to take place. In the case of same amplitude waves, the peaks and troughs of the waves align perfectly, resulting in constructive interference and a larger resultant wave. If the waves have different amplitudes, the interference would be destructive, resulting in a smaller resultant wave.

In conclusion, the behavior of waves during collisions, especially those with the same amplitude, is a complex phenomenon that is governed by fundamental principles of energy and momentum conservation. Further research and study in this area can help us unravel more mysteries of wave dynamics and their fascinating behavior.