# Prosiectau Ffiseg ar gyfer myfyrwyr bl.3 a bl.4

### Wave Propagation in Inhomogeneous Media

#### (supervisor: Balázs Pintér)

Nature of project: theory, software

Available to students on full-time physics degree schemes or joint students.

#### Project description and methodology

Waves are everywhere around us. Without the existence of all sorts of oscillations and waves, our senses would be in trouble. We can feel heat, we can hear, and we can see by waves. Waves are also extremely important in a wide variety of scientific research areas. They are useful diagnostic tools in studying subatomic particles, behaviour of materials, observing phenomena in planetary and solar atmospheres, or discovering distant galaxies. In order to use waves for observations, we have to understand their behaviour in different media. This is what is going to be analysed in the project. The method is a theoretical, mathematical parametric study, through which we can find out how sensitive the wave properties are to homogeneity in the medium where they propagate. The project is suitable for students who like numerical techniques and can confidently programming, preferably in IDL or Python.

A successful project will develop beyond the above in one/some of the following directions:
The original project attempts to solve 'driven problems': assuming that there is a wave source with known properties, the task is to find out how the generated waves will behave in the inhomogeneous medium.

The different cases can also be considered as an 'eigen-value problem', in which the question is what kind of waves can exist in the given medium.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

Additional scope or challenge if taken as a Year-4 project: Adding a magnetic field to the medium will make the problem mathematically much more challenging. Y4 students will do that.

Please speak to Balázs Pintér (bap) if you consider doing this project.

Initial literature for students:

1. Modules on oscillations and waves
2. J.W. Jewett, Jr.R.A. Serway, Physics for Scientists and Engineers, Oxford Univ. Press (Part 2)
3. R.D. Knight, Physics for Scientist & Engineers, Pearson 2004, Chapters 14, 20 and 34.
4. I.S. Grant, W.R. Phillips, The Elements of Physics, Oxford Univ. Press 2002, p. 173-295.

#### Novelty, degree of difficulty and amount of assistance required

This study is new in its comparative nature. It requires preparatory reading and computational skills in Python, IDL, mathCad, Maple or Fortran. The student will gain experience in a comprehensive analytical study and computational modelling of an interesting and highly important physical phenomenon, which appears in almost all fields of physical research.

Supervision and discussions can be done online.

#### Project milestones and deliverables (including timescale)

milestoneto be completed by
-Learning the physics of oscillations and waves (reading, self study)end of October
-Deriving equations that govern physical processes of generating waves (directed work)end of February
-Solving equations analytically and/or numerically (supervised individual work)mid-March
-Drawing conclusions from the results and presenting them with the help of visualisation.Easter