Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

An introduction to television studies. 3rd edition.

This is a comprehensive textbook for students of Television Studies, now updated for its third edition. The book provides students with a framework for understanding the key concepts and main approaches to Television Studies, including audience research, television history and broadcasting policy, and the analytical study of individual programmes. The book includes a glossary of key terms used in the television industry and in the academic study of television, there are suggestions for further reading at the end of each chapter, and chapters include suggested activities for use in class or as assignments. The case studies in the book include analysis of advertisements, approaches to news reporting, television scheduling, and challenges to television in new contexts of viewing on computers and mobile devices. The topics of individual chapters are: studying television, television histories, television cultures, television texts and narratives, television genres and formats, television production, television quality and value, television realities and representation, television censorship and regulation, television audiences, and the likely future for television.