A pulse-echo test on an aluminium alloy block thick (density ) gives longitudinal…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Elastic waves in a solid and at its surface

Problem

A pulse-echo test on an aluminium alloy block

20.0\,\mathrm{mm}

thick (density

2700\,\mathrm{kg\,m^{-3}}

) gives longitudinal echoes every

6.486\,\mathrm{\mu s}

and shear echoes every

12.88\,\mathrm{\mu s}

, each timed to

\pm0.01\,\mathrm{\mu s}

. A slow tensile test on the same alloy gave

E=69.0\,\mathrm{GPa}

. ((a)) Find

E

and

\nu

from the echoes, and the fraction by which the ultrasonic

E

exceeds the tensile value. ((b)) Estimate the adiabatic correction

\Delta E/E

for this alloy at

T=293\,\mathrm{K}

, with

\alpha=23\times10^{-6}\,\mathrm{K^{-1}}

and

c_p=900\,\mathrm{J\,kg^{-1}\,K^{-1}}

. ((c)) Shift each echo time by

0.01\,\mathrm{\mu s}

in the direction that changes

E

most, and find the largest fractional error in

E

the timing allows. Is the difference found in (a) a timing error, or the adiabatic correction?

Browse the problem library