(a) An aluminium plate ( , ) is coupled to water ( ) for an ultrasonic test. At…

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Superposition, boundaries and interference

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

Problem

(a) An aluminium plate (

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

c_L = 6.20\,\mathrm{km\,s^{-1}}

) is coupled to water (

Z_{\rm water} = 1.48\,\mathrm{MRayl}

) for an ultrasonic test. At normal incidence, find the fraction of the longitudinal wave's energy reflected at the aluminium-water interface, and the fraction reflected if the same face were instead exposed to air (take the elastic impedance of air to be negligible compared with that of aluminium). (b) A shallow earthquake occurs in crust that behaves as a Poisson solid with longitudinal speed

c_L = 6.0\,\mathrm{km\,s^{-1}}

. A seismic station records an S-P delay of

15.0\,\mathrm{s}

. Find the distance from the station to the epicentre. (c) A pulse-echo test on an aluminium block of thickness

15.0\,\mathrm{mm}

gives longitudinal and shear back-wall echo intervals of

4.84\,\mu\mathrm{s}

and

9.62\,\mu\mathrm{s}

respectively. Taking

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

, find the shear modulus

G

, Young's modulus

E

and Poisson's ratio

\nu

of the block.

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