## Unidirectional wave motions |

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### Contents

Flexible string movements | 3 |

Discontinuous solutions of the wave equation | 7 |

String profiles with a moving vertex | 12 |

Copyright | |

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### Common terms and phrases

Airy function amplitude approximation assume asymptotic behavior Bessel function boundary conditions characterization complex component consequent constant contour coordinate corresponding cosh density derivative determinations differential equation discontinuity dispersion relation dt dx dx dt dx dx equation of motion estimate excitation expansion explicit exponential expression finite fixed fluid Fourier frequency given Green's function group velocity homogeneous implies incident wave inhomogeneous integral equation interval latter linear load magnitude mass matrix namely obtain oscillator pair parameter partial differential equation particular phase velocity primary wave problem progressive wave range ratio reflection coefficient representation respective satisfy scattering second order sinh solution specific stationary string displacement time-periodic transformation transmission coefficients transverse uniform utilizing vanishes variable variation wave amplitudes wave equation wave factor wave forms wave function wave length wave motions wave number wherein