Derivation of Reflection and Transmission coefficients of wave

In summary, the conversation discusses the process of deriving the reflection and transmission factors between solid-solid interfaces according to Prof. Rose's book "Ultrasonic Waves in Solid Media." The speaker mentions finding mistakes in the chapter but acknowledges that the first two rows in matrix M are correct. They ask for advice on how to obtain the third row in matrix M and the third line in vector a, and if anyone has already done these derivations. The summary explains that the third row in matrix M is derived by finding the derivatives of the reflection and transmission factors with respect to the incident angle, and the third line in vector a is derived by finding the derivatives with respect to the incident wave frequency. It is also mentioned that the chain rule needs to be
  • #1
MiSo
4
0
Hi folks,
I´m trying to derivate the reflection and transmission factor between solid-solid interface according to prof. Rose´s book "ultrasonic waves in solid media". In this chapter, I´ve found there a few mistakes. however the first two rows in matrix M are correct. Can you please give me advice how to obtain, for example, the third row in matrix M and the third line in vector a respectively? Has anyone made the
re derivations? Thank you for help.

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  • #2
The third row in matrix M is derived by finding the derivatives of the reflection and transmission factors with respect to the incident angle. The third line in vector a is derived by finding the derivatives of the reflection and transmission factors with respect to the incident wave frequency. To find the derivatives, you need to use the chain rule. For example, if you want to find the derivative of the reflection factor with respect to the incident angle, you would have to use the chain rule to calculate the derivative of the reflection factor with respect to the incident wave frequency (which is a function of the incident angle) and then calculate the derivative of the incident wave frequency with respect to the incident angle.Hope this helps!
 

Related to Derivation of Reflection and Transmission coefficients of wave

1. What is the purpose of deriving reflection and transmission coefficients of a wave?

The purpose of deriving reflection and transmission coefficients of a wave is to understand how a wave behaves when it encounters a boundary or interface between two different mediums. These coefficients can help predict the amount of energy that is reflected or transmitted at the boundary, which is crucial in various scientific fields such as optics, acoustics, and electromagnetism.

2. How are reflection and transmission coefficients related to each other?

Reflection and transmission coefficients are related by the law of conservation of energy. This means that the sum of the reflected and transmitted energy must equal the incident energy. In other words, the reflection coefficient is equal to 1 minus the transmission coefficient.

3. What factors affect the values of reflection and transmission coefficients?

The values of reflection and transmission coefficients are affected by several factors such as the angle of incidence, the properties of the two mediums, and the polarization of the wave. These coefficients also vary depending on the type of wave, such as electromagnetic, acoustic, or seismic waves.

4. How is the derivation of reflection and transmission coefficients done?

The derivation of reflection and transmission coefficients involves using mathematical equations and principles such as Snell's law, Fresnel's equations, and the boundary conditions of the two mediums. The specific derivation process may vary depending on the type of wave and the properties of the mediums involved.

5. What are some practical applications of reflection and transmission coefficients?

The concept of reflection and transmission coefficients is used in various practical applications, such as designing optical devices, determining the efficiency of acoustic barriers, and analyzing seismic data to understand the Earth's subsurface. These coefficients are also essential in industries such as telecommunications, remote sensing, and medical imaging.

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