## Ultrasound and Elastic Waves: Frequently Asked QuestionsUltrasound has found an increasing number of applications in recent years due to greatly increased computing power. Ultrasound devices are often preferred over other devices because of their lower cost, portability, and non-invasive nature. Patients using ultrasound can avoid the dangers of radiological imaging devices such as x-rays, CT scans, and radioactive media injections. Ultrasound is also a preferred and practical method of detecting material fatique and defects in metals, composites, semiconductors, wood, etc. Detailed appendices contain useful formulas and their derivations, technical details of relevant theories The FAQ format is used where a concept in one answer leads to a new Q&A |

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### Contents

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B THREEDIMENSIONAL SYSTEMS | 155 |

C WAVE EXCITATIONS | 156 |

SOLUTIONS TO THE WAVE EQUATIONS | 160 |

B SEPARATION OF VARIABLES | 164 |

D PLANE WAVE SOLUTIONS | 166 |

DISPERSION GROUP VELOCITY | 170 |

A WAVE PROPAGATION IN VISCOELASTIC MEDIA | 171 |

B WAVE PROPAGATION IN A THICK ROD | 172 |

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WHAT IS A UT BEAM? | 36 |

HOW DOES A PROPAGATING WAVE CHANGE? | 41 |

WAVE INTERACTIONS | 46 |

HOW DOES A WAVE INTERACT WITH A NONUNIFORM OBJECT? | 62 |

HARDWARE EQUIPMENT CONCEPTS | 66 |

SOFTWARE DATA PROCESSING | 86 |

A WHAT ARE THE TYPES OF TIMEDOMAIN ANALYSES? | 87 |

B WHAT ARE THE TYPES OF SPECTRAL ANALYSIS? | 102 |

C WHAT STATISTICAL MEASUREMENTS ARE TAKEN? | 109 |

D WHAT IS IMAGING? | 118 |

STRESS STRAIN AND ELASTICITY ALSO VECTORS AND TENSORS | 122 |

B STRESS | 123 |

C STRAIN | 129 |

D ALTERNATIVE INDICIAL NOTATION | 131 |

THE GENERALIZED HOOKES LAW | 132 |

B STIFFNESS IN ROTATED AXES | 133 |

C SPECIAL CLASSES OF ELASTIC MATERIALS | 134 |

STATES OF STRESS OR STRAIN IN WAVES | 140 |

B UNIAXIAL STRESSSTRAIN RELATIONSHIPS | 144 |

BALANCE OF FORCES AND NEWTONS LAW OF INERTIA | 148 |

A ONEDIMENSIONAL SYSTEM | 149 |

THEORY OF WAVE PROPAGATION | 152 |

C BENDING WAVES | 173 |

TRANSDUCER BEAM FORMING | 176 |

B ANALYSIS OF RADIAL VARIATION OVER BEAM | 177 |

C ANALYSIS OF AXIAL VARIATION OF BEAM STRENGTH | 181 |

SOLUTIONS FOR ANISOTROPY | 184 |

A WAVESPEED | 185 |

B MATERIAL PARTICLE MOTION AND THE PRINCIPAL DIRECTIONS VECTORS | 187 |

C SPECIAL CASES | 188 |

D GROUP VELOCITY | 192 |

OBLIQUE INTERACTIONS BETWEEN WAVES AND BOUNDARIES | 196 |

B OBLIQUE FREE SURFACE REFLECTION OF A TRANSVERSE WAVE | 199 |

C REFRACTION OBLIQUE TRANSMISSION OF A LONGITUDINAL OR TRANSVERSE WAVE | 201 |

D RAYLEIGH WAVES | 202 |

LATERAL STRESS AND STRAIN IN RODS UNDER AXIAL LOADS | 206 |

B THE MINDLINHERRMANN APPROXIMATION | 207 |

BENDING WAVES IN BEAMS AND PLATES | 212 |

B THIN PLATES | 218 |

TIMEDOMAIN ANALYSIS | 222 |

B TIMEDOMAIN SIGNAL CONDITIONING | 224 |

REFERENCES | 230 |

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Ultrasound and Elastic Waves: Frequently Asked Questions Brian M. Lempriere No preview available - 2002 |

### Common terms and phrases

amplitude angle anisotropic applied approximate attenuation axes axial axis beam bending waves called coefficient components of stress configuration convolution cross-section defined deformation depends described determined discussed in Appendix dispersion displacement distance distribution echo effect elastic waves energy excitation factor force free surface function group velocity Hilbert Transform illustrated in Fig impedance incident wave inertia interface isotropic isotropic material later layer longitudinal wave low frequency measurements modulus Mohr's circle motion nondimensional normal stress oblique one-dimensional oscillations peak phase plane wave plate points Poisson's ratio propagating wave pulse radial Rayleigh wave Reflected wave relationship represent rotation S-wave sampling Section shear stress shown in Fig signal Snell's law solution spectrum speed spherical waves stiffness strain surface waves symmetry time-domain transducer transducer diameter transform transmission transmitted wave transverse wave types Typical ultrasonics uniaxial values variation wave FIGURE wave normal wave number wave propagation waveform wavefront wavelength wavespeed x-t diagram zero

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Page 17 - Assessment of flaminability characteristics is extremely complex, since the behavior of materials under fire conditions depends not only on the nature of the material, but also on its thickness and the configuration of the part.

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Page xix - Editors of the Journal of the Acoustical Society of America, the Journal of Applied Physics, and Applied Physics Letters for their permission to reproduce material printed in these journals.

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Page 25 - They are planar and, in some cases, spherical waves, governed only by elasticity and inertia, and are represented by the fundamental (simplest and most general) solutions of the wave equations.