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- W2020731838 abstract "This paper considers the transient propagation of a one-dimensional dilatational wave in a spatially harmonic inhomogeneous medium of semi-infinite extent. A regular perturbation analysis of the response, suitable when the amplitude of the inhomogeneous deviation is small, reveals that inhomogeneity causes backscattering in the second-order term. A temporally harmonic excitation generating a signal whose wavelength is twice the periodicity of the inhomogeneity is shown to lead to a second-order standing wave behind the wave front whose amplitude growth ultimately invalidates the solution. The frequency at which this situation occurs matches the frequency at which Floquet theory predicts instability in the steady-state response. A finite-difference analysis based on the method of characteristics confirms the early-time validity of the perturbation solution. It also reveals that the late-time signal is essentially a standing wave in the region extending outward from the transducer to within several wavelengths of the wave front, whereas it most closely resembles a nondispersive propagating wave in the region of the wave front. [Work supported by NSF.]" @default.
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- W2020731838 modified "2023-10-18" @default.
- W2020731838 title "Transient propagation of a one‐dimensional wave in a harmonically inhomogeneous medium" @default.
- W2020731838 doi "https://doi.org/10.1121/1.2027381" @default.
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