Problem with reflection and transmission of waves

In summary, the conversation discusses the problem of finding a bead in a string with incoming waves, both in the case of x < 0 and 0 < x < L. The concept of transmitted and reflected coefficients is introduced, along with the notation used to represent them. The conversation also touches on the complexities of dealing with a closed room and three-dimensional waves, and the need to keep track of phase and sum the series to produce a resonance curve. It is mentioned that in 3D, the problem can often be separated according to symmetry, resulting in solutions known as Fano resonances.
  • #1
LCSphysicist
646
162
Homework Statement
I will post below an image.
Relevant Equations
There is no actually.
See, to illustrate:
Let's suppose there is an incoming wave by x < 0, what is the problem?

1598017187725.png


It will find a bead in the string, so:

1598017247425.png
, x < 0
1598017267162.png
, x > 0

T and R are the transmitted and reflected coefficients.

Now suppose there is another bead in x = L. The problem is what happens 0 < x < L:

The transmitted wave will be reflected in bead 2, so this reflected wave will be reflected again in the first bead, and so go on...
How to deal with this problem? We really need to deal with this series?

Y = A(T + TR + TRR + TRRR + TRRRR + ...)

(i am just excluding the complex therms to illustrate what i am really asking

notation:

T = transmitted by the first
TR = transmitted by the first, reflected by the second
TRR = transmitted by the first, reflected by the second, reflected by the first
 

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  • #2
The things become worst if we imagine a closed room, and a three dimensional wave... So i think i am missing something.
 
  • #3
Your attachments were difficult to see, so I will pontificate.
The answer is yes you do:
  1. The series need to keep track of phase (i.e. everything is complex)
  2. It is usually trivial to sum and
  3. it produces the resonance curve
I find it some of the most beautiful and simple physics that exists!

In 3D the problem can usually be separated according to symmetry. This gives rise to various solutions, often collectively called Fano resonances. i know (personally) of an excellent treatment of scattering from periodic atomic surfaces with an attractive potential.
 
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Related to Problem with reflection and transmission of waves

1. What is the problem with reflection and transmission of waves?

The problem with reflection and transmission of waves is that when a wave encounters a boundary between two media with different properties, some of the wave energy is reflected back and some is transmitted through the boundary. This can result in a loss of energy and distortion of the original wave.

2. How does the angle of incidence affect reflection and transmission of waves?

The angle of incidence, or the angle at which the wave hits the boundary, affects the amount of energy that is reflected and transmitted. If the angle of incidence is perpendicular to the boundary, all of the energy will be transmitted. However, if the angle of incidence is parallel to the boundary, all of the energy will be reflected.

3. What factors can affect the reflection and transmission of waves?

The properties of the media, such as density and elasticity, can affect the reflection and transmission of waves. The angle of incidence, as well as the frequency and wavelength of the wave, can also play a role in how much energy is reflected and transmitted.

4. How can the problem of reflection and transmission of waves be minimized?

One way to minimize the problem of reflection and transmission of waves is by using materials with similar properties on either side of the boundary. This can help reduce the amount of energy that is reflected and transmitted. Additionally, using materials that absorb or dampen the wave energy can also help minimize the problem.

5. Can the problem of reflection and transmission of waves be completely eliminated?

No, the problem of reflection and transmission of waves cannot be completely eliminated. However, it can be reduced by using appropriate materials and angles of incidence. Some amount of reflection and transmission is inevitable, but it can be managed and minimized to improve the overall quality of the wave.

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