Wave theory and applications
This textbook provides a modern introduction to wave theory and its applications to physical phenomena such as deep water waves, transmission lines, elasticity, and traffic flow. The author presents a broad coverage of the subject, including numerous exercises. Each of the main topics is described in detail with examples of their applications. These topics include the classical wave equation, dispersion, dissipation, interconnected waves, diffusive waves, and first and second order non-linear waves. The special attention paid to non-linear and elastic waves represents a major strength of the text, along with its inclusion of an entire chapter devoted to the use of characteristics and asymptotic expansions. Intended for advanced undergraduates, the book will also be of interest to instructors in mathematics, physics and engineering courses.
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TRANSVERSE VIBRATIONS ON STRINGS
LONG WAVES ON CANALS
SURFACE WAVES ON RELATIVELY
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air resistance amplitude approximation attenuation boundary conditions cable canal characteristic velocity classical wave equation coeﬂicient components constant proﬁle cosh curve deﬁned denotes density discontinuity dispersion equation displacement vector equal erfc Exercise exponential ﬁnd ﬁnite ﬁrst ﬁrst order ﬁxed ﬂow Fourier sine series frequency function given by eqn gives governing equations grad group velocity harmonic waves heat conduction Hence incident wave inﬁnite initial conditions integral isentropic kinetic Laplace transform linear longitudinal waves mathematical non-linear non-zero partial differential equations phase constant plane positive sense potential energy r.h.s. of eqn reﬂected wave respectively satisﬁed separation of variables shock sinh sinusoidal solution of eqn string Substitute from eqns Substituting back Substituting in eqn surface tanh theory total energy transmitted wave transverse variables vibration wave equation wave travels wave velocity wavelength x-direction zero