This thesis contains a summary of the research I have done as part of the first two years of my PhD study and a plan for the research I intend to conduct as part of the remaining two years of my 4+4 PhD. It contains detailed summaries of two papers. The first paper is published and treats magnetic pseudodifferential operators and their spectral properties. The second paper is unpublished and treats the acoustic phenomenon known as acoustic black holes and considers optimization of the height profile of acoustic black holes.