The original work presented in this thesis pertains to the design and characterisation of resonant-cavity-based acoustic metamaterials, with a focus on airborne sound. There are five separate experimental chapters, each with a unique approach to the design of periodic structures that can support and manipulate air-bound acoustic surface waves via diffractive coupling between resonant-cavities. The first two chapters concern measurement of the acoustic transmission though various kinds of periodic slit-arrays, whilst the latter three chapters utilise a near-field imaging technique to directly record and characterise the dispersion of trapped acoustic surface waves. The first experimental chapter investigates the effect that thermodynamic boundary layers have on the Fabry-Perot-like cavity resonances that are so often utilised in acoustic metamaterial design. At audio frequencies, these boundary layers have a decay length that is typically more than two orders of magnitude smaller than the width of the resonating slit-cavities, hence it may naively be assumed that their effect can be ignored. However, by studying in detail the effect that reducing slit-cavity width has on the frequency of the measured cavity-resonance, for both a single slit cavity and a slit-cavity array, it is found that these boundary layer effects become significant on a far larger scale than their characteristic thickness. This is manifested in the form of a reduction in the resonant frequency as the slit-width is narrowed. Significant attenuation of the resonance and a 5% reduction in the effective speed of sound through the cavity is measured when the boundary layers form only 5% of the total width of each slit. Hence, it is both shown that the prevalent loss free treatment of acoustic slit-cavities is unrealistic, and that one may control the effective speed of sound through the slit-cavities with a simple change in slit-width. The second chapter explores the effect of ‘compound’ grating structure on trapped acoustic surface waves, a compound grating having a basis comprised of more than one resonating element. The angle dependent acoustic transmission spectra of four types of aluminium slit-array are recorded, and for the compound gratings, it is found that sharp dips appear in the spectra that result from the excitation of a ‘phase-resonance’. This occurs as new degrees-of-freedom available to the acoustic near-field allow the fields of adjacent cavities within a unit-cell to be both out-of-phase and strongly enhanced. By mapping the transmission spectra as a function of in-plane wavevector, the dispersions of the modes supported by each sample are determined. Hence, the origin of the phase-resonant features may be described as acoustic surface waves that have been band-folded back into the radiative regime via diffraction from higher in-plane wavevectors than possible on a simple grating. One of the samples is then optimised via numerical methods that account for thermodynamic boundary layer attenuation, resulting in the excitation of a sharp, deep transmission minimum in a broad maximum that may be useful in the design of an acoustic filter. The third chapter introduces the near-field imaging technique that can be utilised to directly characterise acoustic surface waves, via spatial fast Fourier transform algorithms of high-resolution pressure field maps. The acoustic response of a square-lattice open-ended hole array is thus characterised. It is found that over a narrow frequency band, the lattice symmetry causes the acoustic surface power flow to be channelled into specific, predictable directions, forming ‘beams’ with a well defined width. In chapter four, the existence of the ‘acoustic line mode’ is demonstrated, a type of acoustic surface wave that may be supported by a simple line of open-ended hole cavities. The near-field imagine technique is again used to extract the mode dispersion. This acoustic line mode may be readily manipulated, demonstrated by arrangement of the line of holes into the shape of a ring. The existence of this type of mode offers a great deal of potential for the control of acoustic energy. Chapter five explores the effect of ‘glide-symmetry’ on a pair of acoustic line modes arranged side-by-side. A control sample not possessing glide- symmetry is first characterised, where measurement of the acoustic near- fields show that this sample supports two separate modes at different frequencies, with their phase either symmetric or anti-symmetric about the mirror plane between the lines of holes. One of these lines is then shifted along its periodicity by half of a grating pitch, thus creating glide-symmetry. The resulting sample is found to support a single hybrid mode, capable of reaching a much larger in-plane wavevector than possible on a simple grating with no gaps in its band-structure, and displaying a region of negative dispersion. The third sample demonstrates how one may increase the coupling strength between the two lines of holes via manipulation of the cavity shape, thus enhancing the glide-symmetry effect. The thesis concludes with preliminary investigations into other possible ways of manipulating acoustic surface waves, such as with the use of ‘screw-symmetry’.