Wave Motion

MATH35012 Wave Motion 10 Semester 2 Undergraduate Level 3 Richard Hewitt Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 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. 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. This course unit aims to elucidate some of the physical properties of important types of wave motion and their mathematical descriptions. On successful completion of this course unit students will be able:   <ul> <li> Define the basic kinematic properties of a wave.</li> <li> Describe and classify the physical properties of a wave from its mathematical form.</li> <li> Derive the dispersion relation for a range of wave problems.</li> <li> Analyze the dispersion relation to draw physical conclusions.</li> <li> Formulate a mathematical problem for a physically-described system, including (but not restricted to) the examples of elastic, water and sound waves.</li> <li> Apply the methods of the course to previously unseen wave problems and variations of seen problems.</li> </ul> 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] 0 Other 20% 1 Written exam 80% <ul> <li> Coursework: One take-home question, weighting 20%</li> <li> End of semester examination: weighting 80%</li> </ul> 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. MATH24420 Partial Differential Equations & Vector Calculus Pre-Requisite Compulsory PHYS20171 Mathematics of Waves and Fields Pre-Requisite Compulsory MATH20401 Partial Differential Equations and Vector Calculus A Pre-Requisite Compulsory MATH20411 Partial Differential Equations and Vector Calculus B Pre-Requisite Compulsory MATH35012 Pre-Requisites: MATH24420 (OR PHYS20171, OR MATH20401/11)PHYS20171 is an acceptable alternative for those Maths-Physics students who took that unit instead of MATH24420. N 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. Lectures 12 Tutorials 12 0 76