Join us on an alphabetical journey through the research themes and key concepts behind our work.
We will add new entries to this list regularly, so keep checking in to find out more!
We will add new entries to this list regularly, so keep checking in to find out more!
A is for Acoustics
Sound is all around us: it accompanies everything we do. Human beings are both sources and the receivers of sounds. Acoustics is the branch of science and engineering concerned with all aspects of sound, including its generation and transmission, its control and use, and its effects on people and the environment.
The scientific study of sound dates at least as far back as the 6th century BCE, with experiments by Greek philosopher and mathematician Pythagoras into harmonics and vibrating strings [1]. Several centuries later, the Roman engineer and architect Vitruvius (d. 15 BCE) is credited with the first formal treatment of architectural acoustics in his multivolume work De Architectura, in which he discusses sound propagation in theatres [2].
The use of the term “acoustics” to define a branch of science came much later. Although the word had been used in the context of sound previously [3], the definition is usually attributed to physicist and mathematician Joseph Sauveur, who in 1701 proposed a new field of study called acoustique. He described his new discipline as “a science superior to music”, because it encompassed all sound, not simply music and harmonics [4].
The use of the term “acoustics” to define a branch of science came much later. Although the word had been used in the context of sound previously [3], the definition is usually attributed to physicist and mathematician Joseph Sauveur, who in 1701 proposed a new field of study called acoustique. He described his new discipline as “a science superior to music”, because it encompassed all sound, not simply music and harmonics [4].
When we think about acoustics the first thing that springs to mind might be architectural acoustics, and the optimisation of indoor sound. However, modern acoustics is a multidisciplinary field, encompassing physics, material science, engineering, psychology, physiology, music, architecture, neuroscience, environmental science and mathematics. Some of the many other branches of acoustics include:
Physical acoustics: Physical acoustics overlaps with other fields of acoustics such as engineering and medical imaging. It also encompasses sound beyond the human audible range. Frequencies below the audible are called infrasound. Many natural phenomena such as earthquakes and thunder generate infrasound. Higher frequency sound is ultrasound, whose uses in medical imaging are well known. There are many other interesting physical acoustic phenomena, such as the photoacoustic effect: where sound is generated by the interaction of light with matter.
Musical acoustics: This is a broad field encompassing the design of musical instruments, building acoustics, the human perception of sound and music, and music recording and reproduction.
Psychoacoustics and physiological acoustics: These include the study of people's perception of sound and its physical and pshychological impact on us, and the physiology of hearing and hearingloss.
Underwater acoustics and oceanography: The study of underwater acoustics and sonar has military and commercial applications, while in marine biology, acoustics can lead to a better understanding of animal communication, and the effect of humangenerated noise on marine animals.
Environmental noise control: We know that exposure to loud noise can cause hearing loss, but this is not the only adverse effect. Noise can reduce our quality of life, and even our life expectancy, causing an estimated 12,000 premature deaths in Europe each year [7]. For this reason, noise reduction and control is an extremely active branch of acoustics.
Musical acoustics: This is a broad field encompassing the design of musical instruments, building acoustics, the human perception of sound and music, and music recording and reproduction.
Psychoacoustics and physiological acoustics: These include the study of people's perception of sound and its physical and pshychological impact on us, and the physiology of hearing and hearingloss.
Underwater acoustics and oceanography: The study of underwater acoustics and sonar has military and commercial applications, while in marine biology, acoustics can lead to a better understanding of animal communication, and the effect of humangenerated noise on marine animals.
Environmental noise control: We know that exposure to loud noise can cause hearing loss, but this is not the only adverse effect. Noise can reduce our quality of life, and even our life expectancy, causing an estimated 12,000 premature deaths in Europe each year [7]. For this reason, noise reduction and control is an extremely active branch of acoustics.

Researchers in the Mathematics of Waves and Materials group apply mathematical modelling to acoustics. Research themes include the design of acoustic metamaterials and phononic crystals: materials whose properties are determined by their structures, rather than their chemical composition. Acoustic metamaterials have structural elements that are smaller than the wavelengths of the sounds they are designed to interact with. This leads to properties that are not found in conventional materials. Other areas of acoustical research within the group include aero and hydroacoustics: the study of the noise generated by fluid flows both on their own (jet noise) and when interacting with solid boundaries (trailing edge noise) in air and water, and the interaction of soundwaves with materials, including nanofibrous materials.

20202021 is the International Year of Sound, a global initiative to highlight the importance of sound and acoustics in society. You can find learning resources and events from acoustics organisations around the world on the Year of Sound website.
[1] Zhmud, L. (2012) "8: Harmonics and Acoustics in Pythagoras and the Early Pythagoreans", Oxford Scholarship Online
[2] Maconie, R. (2005) "Musical Acoustics in the age of Vitruvius", Musical Times; London, 146: 7582.
[3] Dostrovsky, S. (2008) "Sauveur, Joseph", in Complete Dictionary of Scientific Biography vol. 12, New York, NY: Charles Scribner's Sons, 127129.
[4] Fix, A. (2015) "A Science Superior to Music: Joseph Sauveur and the Estrangement between Music and Acoustics", Phys. Perspect., 17: 173–197.
[5] Rossing, T. D (2014) "A Brief History of Acoustics" in Springer Handbook of Acoustics. New York, NY: Springer, 924
[6] Rossing T.D. (2014) "Introduction to Acoustics" in Springer Handbook of Acoustics. New York, NY: Springer, 16
[7] European Environment Agency, Environmental noise in Europe — 2020, EEA Report No 22/2019
[2] Maconie, R. (2005) "Musical Acoustics in the age of Vitruvius", Musical Times; London, 146: 7582.
[3] Dostrovsky, S. (2008) "Sauveur, Joseph", in Complete Dictionary of Scientific Biography vol. 12, New York, NY: Charles Scribner's Sons, 127129.
[4] Fix, A. (2015) "A Science Superior to Music: Joseph Sauveur and the Estrangement between Music and Acoustics", Phys. Perspect., 17: 173–197.
[5] Rossing, T. D (2014) "A Brief History of Acoustics" in Springer Handbook of Acoustics. New York, NY: Springer, 924
[6] Rossing T.D. (2014) "Introduction to Acoustics" in Springer Handbook of Acoustics. New York, NY: Springer, 16
[7] European Environment Agency, Environmental noise in Europe — 2020, EEA Report No 22/2019
B is for Boundary Conditions
Just as in high school mathematics or physics, where one imposes conditions on the solution to an ordinary differential equation (such as a simple harmonic oscillator), in continuum mechanics boundary conditions are imposed on the solutions to partial differential equations which represent mathematically the laws governing the generic behaviour of particular materials.
A familiar example is the dripping of a tap. As water slowly accumulates at the outlet of the tap, its surface forms a smooth nearspherical shape as a consequence of surface tension acting to minimize the exposed surface area. Eventually, it becomes energetically expedient for a drop to detach and fall away, and the process repeats. The partial differential equations in this context are the NavierStokes equations, and the boundary conditions are the surface tension at the interface between water and air, the pressure gradient or the flow rate within the tap, and also the contact conditions at the meeting point between water, air, and the tap itself. In general, the flow of water, or any Newtonian fluid, is a function only of the Reynolds number and the boundary conditions.

The refraction of a light ray as it passes from one medium into another can also be understood in terms of boundary conditions applied at the interface between the two media. Solving the EulerLagrange equation, one can show that \(\frac{sin \theta}{c}\) must be the same on either side of the boundary, where θ is the angle of incidence on one side and the angle of refraction on the other side, and c is the local speed of light in each medium. This result is known as Snell's Law, although it was described by Ibn Sahl almost 600 years before Snell was born [1].

The extent to which the full detail of the boundaries are incorporated within a mathematical model can depend on whether there is a practical need for a quantitative result in a particular case, for example, the stress on a rocket's nose cone, or the circulation of air in a hospital. If the intention of the modelling is mainly to understand the underlying phenomena in a more qualitative sense, then an idealized and representative form of the problem is often developed, typically involving simplifications in the form of assumptions about spatial symmetry, infinite extent, or smoothness of walls etc. Such simplifications are usually intended to allow a certain amount of progress with a purely analytical approach, or for testing of a computational approach at a proof of concept stage. Solving the fundamental equations in full generality may be impossible, but with restrictions on the possible solutions, e.g. an assumption of spherical symmetry, or taking an asymptotic limit in terms of a small parameter, the problem may become tractable. In effect, the simplifications can be interpreted as modifying the boundary conditions. Then the relevance of the idealized solution in the context of the full unsimplified problem will depend on whether the boundary conditions are amenable to the sort of simplifications discussed.
When assessing the robustness and accuracy of a new computational algorithm, certain wellstudied and sometimes challenging combinations of boundary conditions are used, known as benchmark problems. These are problems for which the correct solutions are known, and the idea is to highlight any limitations of the algorithm, or any mistakes made in its implementation. For example, the liddriven cavity is a standard benchmark problem in CFD (computational fluid dynamics) for the validation of numerical methods [2].
When assessing the robustness and accuracy of a new computational algorithm, certain wellstudied and sometimes challenging combinations of boundary conditions are used, known as benchmark problems. These are problems for which the correct solutions are known, and the idea is to highlight any limitations of the algorithm, or any mistakes made in its implementation. For example, the liddriven cavity is a standard benchmark problem in CFD (computational fluid dynamics) for the validation of numerical methods [2].
N. F. Morrison

[1] Rashed, R. (1990) "A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses", Isis, 81(3): 464491
[2] Hinch, E. J. (2020) "1: The Driven Cavity" in Think Before You Compute. Cambridge: Cambridge University Press, 38
[2] Hinch, E. J. (2020) "1: The Driven Cavity" in Think Before You Compute. Cambridge: Cambridge University Press, 38