## Nonlinear acoustic behavior at a caustic |

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### Contents

FORMAL SOLUTION OF THE CAUSTIC EQUATION | 6 |

THE SOLUTION FOR A DISCONTINUOUS SIGNAL | 13 |

SIMPLE WAVES AND SHOCK WAVES 1 6 | 16 |

4 other sections not shown

### Common terms and phrases

Abramowitz and Stegun appendix section approximate arctangent boundary conditions caustic problem caustic region characteristic constant contours continuous discontinuity discussed in Chapter divergence theorem equations 20 exact solution fit a shock function subprogram geometric functions given governing equation Hayes Heaviside function Hence hypergeometric functions hypergeometric series incoming signal Jacobian limit line linear solution listed in Table Location of shock logarithmic singularities mathematical Maximum pressure coefficient minimum y values multi-valued function multi-valued region Newton's method NONLINEAR ACOUSTIC BEHAVIOR path physical interest physical x,y Rankine-Hugoniot relations reflected signal region in physical region of graph satisfied Seebass series evaluations shock in multi-valued shock locations shown shock wave simple wave region simple wave theory single-valued smoothed step function sonic boom sonic line specified steepens step function pulse stream function Subroutine supersonic transformation formulae Tricomi equation u-based Ug and Vg UVCALC v-based shock Velocity component velocity potential