From Room Acoustics to Ultrasound – Modeling, Simulation and Measurements

With our course on acoustics, we would like to take you on a journey through the secrets of acoustics. Starting at the mathematical formulation of the underlying physics, we move over to numerical simulations and perform on-site practical experiments. Thereby, we do not only keep the later application in mind but also the physiological effects of sound onto living beings. With this broad spectrum, we want to attract motivated students from a wide range of disciplines going from theoretical physics and mathematics over natural sciences and experimental studies to various kinds of engineering and computer science. (In the last years we always had an excellent combination of these competences, so that the course was colourful and attracting.)

Acoustical phenomena are governed by partial differential equations (PDEs) describing the propagation of sound in fluids and solids. In order to derive a set of PDEs that is appropriate for later theoretical and numerical analysis, we have to start by discussing the materials and their constituents (porous materials, foams, air, solids). Secondly the systems, like three-dimensional volumes, plates or membranes have to be understood regarding transmission, radiation or absorption. They can be designed for optimizing specific acoustical characteristics, e.g. for optimally transmitting music in a hall by well arranged surfaces, for perfectly radiating and receiving ultrasound by adequate vibrating membranes or plates, or for a well-designed extraction or filtering of energy by meta materials. Thirdly the impact of sound onto living beings and structure - the perception - and the desired application play an important role. Depending on the type of signal and problem a description in the time or frequency domain or even both is relevant. We show that in investigations on room acoustics a time domain analysis might be important in order to reflect the acoustical behaviour in the light of physiological aspects of the human perception whereas in machinery acoustics, frequency domain approaches might be much more appropriate as they simplify the treatment of the governing equations. For ultrasound applications, finally, the radiation pattern of transducers is to be determined in the frequency domain before transient analysis is performed to investigate on pulse-echo behaviour.

In the further course of our journey, you will learn that classical numerical approaches based on displacements and stresses like the finite element approach (FEM) or the boundary element approach (BEM) reach limits especially if the ratio between wavelength and geometrical dimensions grows large. In such cases, additional methods - like the statistical energy analysis (SEA) which is based on the averaging of energetic values, the spatial impulse response method (SIR) or hybrid schemes like the coupling between FEM and acoustical raytracing – have to be applied. However, these methods shall not only be discussed in theory. Instead, you will be given the chance to perform your own numerical investigations using a set of provided tools (Matlab, Ansys, Field II, NACS).

Last but not least, on-site experiments will connect the learned theoretical knowledge with practical experience. For this year, we have planned a hand-full of experiments that are in step with actual practice including reverberation time measurements inside the village's chapel and ultrasound pulse-echo measurments in air and under water. Additionally, we intend to repeat an experimental highlight from our last course that found high popularity among the students. We don't want to reveal too much yet but what about having the possibility to listen through a closed window? And don't get us wrong: These experiments will be prepared and performed by yourselves!

We hope to have awaken your interest on acoustics and look forward to your participation.