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- Visualization of acoustic waves in air and subsequent audio recovery with a high-speed schlieren imaging system: Experimental and computational development of a schlieren microphone
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We present a high-speed single-mirror double-pass coincident schlieren system and corresponding algorithms for the visualization of acoustic waves and recovery of their associated audio signals. Schlieren systems are extensively used to visualize strong shockwaves, such as those from supersonic motion or explosions. Recently, they have also been used to visualize lower amplitude non-linear acoustic phenomena, such as the weak shockwaves arising from impact events including hand claps, belt snaps, and towel cracks. Time-invariant sounds produced by loudspeakers have also been imaged, in one case leading to frequency analysis, although these have been limited to high-frequency signals at very high sound pressure levels. The research presented here shifts the focus from sound-field visualization towards audio signal recovery. A comprehensive exploration of several parameters for imaging sound sources, including frequency, wave form, and amplitude, is presented. In addition, we address for the first time the recovery of phase information, which would be essential for speech intelligibility, and the more general case of non-contact sound field reconstruction. Through image and signal processing, it is shown that audio signals can be recovered from high-speed schlieren video whose acoustic waves appear to be below the limit of visibility, and were previously deemed unrecoverable by virtue of their frequency and sound pressure level. This includes sounds at frequencies and loudnesses relevant for human hearing, producing the first ‘schlieren microphone’.
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- Bow-shaped caustics from conical prisms: a th-century account of rainbow formation from Robert Grosseteste’s De iride
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The rainbow has been the subject of discussion across a variety of historical periods and cultures, and numerous optical explanations have been suggested. Here, we further explore the scientific treatise De iride [On the Rainbow] written by Robert Grosseteste in the 13th century. Attempting to account for the shape of the rainbow, Grosseteste bases his explanation on the optical properties of transparent cones, which he claims can give rise to arc-shaped projections through refraction. By stating that atmospheric phenomena are reducible to the geometric optics of a conical prism, the De iride lays out a coherent and testable hypothesis. Through both physical experiment and physics-based simulation, we present a novel characterization of cone–light interactions, demonstrating that transparent cones do indeed give rise to bow-shaped caustics—a nonintuitive phenomenon that suggests Grosseteste’s theory of the rainbow is likely to have been grounded in observation.
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- A thirteenth-century theory of speech
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This historical paper examines a pioneering theory of speech production and perception from the thirteenth century. Robert Grosseteste (c.1175—1253) was a celebrated medieval thinker, who developed an impressive corpus of treatises on the natural world. This paper looks at his treatise on sound and phonetics, De generatione sonorum [On the Generation of Sounds]. Through interdisciplinary analysis of the text, this paper finds a theory of vowel production and perception that is notably mathematical, with a formulation of vowel space rooted in combinatorics. Specifically, Grosseteste constructs a categorical space comprising three fundamental types of movements pertaining to the vocal apparatus: linear, circular, and dilational-constrictional; these correspond to similarity transformations of translation, rotation, and uniform scaling, respectively. That Grosseteste's space is categorical, and low-dimensional, is remarkable vis-a-vis current theories of phoneme perception. As well as his description of vowel space, Grosseteste also sets out a hypothetical framework of multisensory integration, uniting the production, perception, and representation in writing of vowels with a set of geometric figures associated with “mental images.” This has clear resonances with contemporary studies of motor facilitation during speech perception and audiovisual speech. This paper additionally provides an experimental foray, illustrating the coherence of mathematical and scientific thinking underpinning this early theory.
