Prediction, detection and characterization of a fast surface wave produced near the first critical angle

Prediction, detection and characterization of a fast surface wave produced near the first critical angle J.C. COUCHMAN and J.R. B E L L The surface wave predicted by acoustical theory that is supposed to appear at the first critical angle was detected by an experiment through which its speed, amplitude, and attenuation rates were measured. Although very low in amplitude, the fast surface wave detected near the first critical angle for a water-aluminium interface. The surface wave was observed to travel at the compressional wave velocity and was less attenuated in its travel than was the pseudo-Rayleigh wave. Introduction Classical acoustical theory gives imaginary amplitudes for the refracted compressional wave beyond the first critical angle and for both the refracted compressional and shear waves beyond the second critical angle. ~ The latter imaginary solutions correspond to the psuedo-Rayleigh wave (or break-away wave) which is produced by a phase change in the reflected waves and which travels along the surface at the Rayleigh velocity. The presence or properties of the surface wave beyond the first critical angle does not appear to be discussed in the literature, although Breazeale 2 reports observing surface waves above the critical angle in sediment, and Adler 3 has observed surface waves above the longitudinal critical angle at the water-plexiglass interface. The imaginary solutions for the amplitudes of the transmitted longitudinal and shear waves for the well known boundary value problem involving a compressional wave obliquely incident on aluminium at a water-aluminium interface are plotted in Fig. 1. This result shows that a surface wave should be present at about 14° and it should have about two orders of magnitude less amplitude than the pseudo-Rayleigh wave. An experiment was performed to detect and characterize the first surface wave.

Experi mental m e t h o d The experimental configuration set up in an immersion tank is shown in Fig. 2. Two 15 MHz broadband transducers were used which produce 6.35mm diameter collimated beams. The transducer on the left was mounted so the angle of incidence could be varied. Ultrasound was propagated along the surface and re-emitted from the edge of a large aluminium block. Times of arrival and amplitudes of received ultrasound were measured and recorded at several angles of incidence beginning with the first detectable signal and ending at about 40 ° . One set of measurements was made at Xo cm from the edge of the block and two others were made at Xo + 2.54 cm and Xo + 5.08 cm. authors are at General Dynamics, Fort Worth Division, PO Box 748, Fort Worth, Texas 76101, USA. Paper received 21 February

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This experiment was not designed to measure the initial amplitude of surface waves that could be directly compared with the theoretical predictions plotted in Fig. 1, because of the dependence of l and w upon Xo and 0. Results were expected to (1) provide a qualitative indication of whether the first surface wave could be detected, (2) provide an indication of its amplitude relative to the second surface wave (the pseudo-Rayleigh wave), (3) to provide a measure of its velocity along the water/aluminium interface, and (4) to estimate relative attenuation rates.

Experimental results The relative amplitudes measured are plotted in Fig. 3. It was found that a fast ultrasonic signal was detected after the angle of incidence exceeded 8°. This signal reached a maximum amplitude near the first critical angle and then

0041-624X/78/060272-03 $02.00 © 1978 IPC BusinessP r e s s

ULTRASONICS. NOVEMBER 1978

fell in amplitude until it became hidden in electronic noise. A second, slower ultrasonic signal appeared before the faster signal faded away and it grew to maximum amplitude at around 31 ° or 32 ° angle-of-incidence.

angle of incidence and the distance interval over which they were measured. The fast surface wave can be seen to attenuate more slowly than the slower surface wave and each attenuates most rapidly as it nears the first and second critical angles.

All signals detected reduced in amplitude as the distance Xo was increased. This amplitude reduction was used to estimate attenuation coefficients 'a' for the surface waves. Three values of e were computed as follows:

The velocities of sound were computed from the measurements made and were found (see Fig. 5) to be approximately the longitudinal wave velocity for the first surface wave but between the Rayleigh velocity and the shear wave velocity for the second surface wave.

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U L T R A S O N I C S . N O V E M B E R 1978

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Fig. 5 The v e l o c i t y of the surface wave near the first critical angle was the same as the compressional wave v e l o c i t y in a l u m i n i u m . The surface wave at the second critical angle travelled at the Rayleigh wave v e l o c i t y

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Conclusions The surface wave predicted by acoustic theory does exist near the first critical angle. It has an amplitude about two orders of magnitude lower than the pseudo-Rayleigh wave in accordance with acoustic theory. It is less attenuated than the pseudo-Rayleigh wave as it travels along the water• aluminium interface at the velocity of a conventional compressional wave in aluminium.

274

References 1 2

3

Couehman, J.C., Yee, B.G.W., Chang, F.H. 'Energy Partitioning of Ultrasonic Waves Beyond the Critical Angle of Flat Boundaries', Ultrasonics 12 (2) (1974)69-71 Breazeale,M.A., BjOrn0,L. 'Forward and Backward Displacement of Ultrasonic Waves Reflected from A Water-Sediment Interface', Proc Ultrasonics Intern 77, IPC Science and Technology Press (1977) 440-447 Adler, L. Associate Professor at the University of Tennessee, Private communication - findings to be published.

ULTRASONICS. NOVEMBER 1978