# BSc Mathematics

Year of entry: 2022

## Course unit details:Wave Motion

Unit code MATH35012 10 Level 3 Semester 2 Department of Mathematics No

### Overview

Wave motion occurs in the oceans, atmosphere and in the earth. Problems of wave production and transmission, of wave harnessing or shielding, and of detection will always be of interest. This is a large and important subject area which this course unit can only begin to study, nevertheless this beginning will contain ideas and techniques applicable to a broad range of wave motion.

### Aims

This course unit aims to elucidate some of the physical properties of important types of wave motion and their mathematical descriptions.

### Learning outcomes

On successful completion of this course unit students will be able:

• Define the basic kinematic properties of a wave.
• Describe and classify the physical properties of a wave from its mathematical form.
• Derive the dispersion relation for a range of wave problems.
• Analyze the dispersion relation to draw physical conclusions.
• Formulate a mathematical problem for a physically-described system, including (but not restricted to) the examples of elastic, water and sound waves.
• Apply the methods of the course to previously unseen wave problems and variations of seen problems.

### Syllabus

1.Introduction: wave kinematics. [1 lecture]

2.Waves on a stretched string. [1]

3.Free surface water waves: Standing/progressive waves, dispersion relations for infinite and finite depth layers. [10]

4.Surface tension effects. [2]

5.Waves in a continuously stratified fluid: internal gravity waves. [2]

6.Sound waves. [8]

### Assessment methods

Method Weight
Other 20%
Written exam 80%
• Coursework: One take-home question, weighting 20%
• End of semester examination: weighting 80%

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

No text book is required and all material will be provided in the lecture notes. For those wishing to do further reading, then some appropriate books are

J.J. Stoker, Water Waves, Wiley, 1958.

M.J. Lighthill, Waves in Fluids, Cambridge, 1979.

### Study hours

Scheduled activity hours
Lectures 12
Tutorials 12
Independent study hours
Independent study 76

### Teaching staff

Staff member Role
Richard Hewitt Unit coordinator

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

•         You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently
•         You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week
•         There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises
•         In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.
The remaining independent study time comprises revision for and taking the end-of-semester assessment.

The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.