Wave Equation After Reflection

In summary, the components of the given equation represent a wave that has been reflected off a wall. The ∅ represents the phase change, while wt indicates the change in direction of the wave. The actual reflected wave would be represented as A\cos\left(-kx+\omega t + \phi'\right) to signify the negative direction and absorb the sign change in \phi' into \phi.
  • #1
elemis
163
1
What do the components of the following equation represent :

http://www.mediafire.com/view/?0we6f9jkw26qi9o

To be clear, this represents a wave of the form Acos(kx-wt) after being reflected off a wall.

I understand that the ∅ represents the phase change of the wave after hitting the wall. The wt is now positive instead of negative because it is traveling in the opposite direction.

Is this a correct description or have I missed something out ?
 
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  • #2
Seems about right. But I would point out that the actual reflected wave would be something like, [itex]A\cos\left(-kx+\omega t + \phi'\right)[/itex] to actually signify that the wave is moving in the negative x direction due to the reflection. One can then use the properties of the cosine to flip the sign of the argument and absorb the sign change in \phi' into \phi.
 

1. What is the wave equation after reflection?

The wave equation after reflection is a mathematical formula that describes the behavior of a wave after it reflects off of a boundary or obstacle. It takes into account factors such as the wave's frequency, wavelength, and the properties of the medium it is traveling through.

2. How is the wave equation after reflection different from the original wave equation?

The original wave equation describes the behavior of a wave as it travels through a medium without any reflections. The wave equation after reflection takes into account the changes in the wave's properties after it reflects off a boundary, such as changes in amplitude, frequency, and direction.

3. What are the key variables in the wave equation after reflection?

The key variables in the wave equation after reflection include the incident angle of the wave, the angle of reflection, the frequency and wavelength of the wave, and the properties of the medium it is traveling through, such as density and elasticity.

4. How is the wave equation after reflection used in real-world applications?

The wave equation after reflection is used in various fields such as acoustics, optics, and seismology to understand the behavior of waves as they interact with different materials and boundaries. It is also used in engineering and design to predict and mitigate the effects of reflections in structures and systems.

5. Are there any limitations to the wave equation after reflection?

Like any mathematical model, the wave equation after reflection has its limitations. It assumes that the reflecting surface is smooth and the medium is homogeneous, which may not always be the case in real-world scenarios. Additionally, it does not take into account other factors that may affect wave behavior, such as diffraction and interference.

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