## Wave Motion

 Unit code: MATH35012 Credit Rating: 10 Unit level: Level 3 Teaching period(s): Semester 2 Offered by School of Mathematics Available as a free choice unit?: N

None

#### Aims

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

#### 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.

#### 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.

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

• Coursework: One take-home question, given in the week before the Easter break, returned in Week 9, weighting 20%
• End of semester examination: two hours weighting 80%

#### 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]

• J.J. Stoker, Water Waves, Wiley, 1958.
• M.J. Lighthill, Waves in Fluids, Cambridge, 1979.

#### 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.

#### Study hours

• Lectures - 22 hours
• Tutorials - 11 hours
• Independent study hours - 67 hours

#### Teaching staff

Richard Hewitt - Unit coordinator