Are there any minima?

Abstract

Reflection of ultrasound from a cylindrical hole is discussed. A cylindrical side hole is an artificial flaw that is very convenient for tuning a flaw detector. It can be easily made with high precision, while reflection from it is independent of the input angle. This reflector is good in all respects, but it still has a significant drawback. Alexander Sergeevich Golubev, who has now passed on, used the diffraction theory to calculate the dependence of reflection amplitude B on cylinder diameter d (1), and more precisely, on the ratio d / λ of the cylinder diameter to the ultrasonic wavelength. It was found that the amplitude increased monotonically with an increase in diameter, in agreement with the beam approximation for longitudinal waves, but the amplitude varied nonmonotonically for transverse waves: namely, there were pronounced minima and max- ima (see figure, curve 1 ). Of course, a cylindrical side hole cannot be used for tuning the sensitivity of equip- ment in a region with nonmonotonic behavior. Later, many researchers studied reflection from a cylindrical side hole and found that the nonmonotonic behavior originates from run-round and slide-off waves. A transverse wave near a hole's surface propagates as a wave running around the hole. It generates a transverse wave that slides along a tangent to the hole's surface. At hole diameters that are much larger than the transverse wavelength, a run-round headwave and a slide-off wave in the form of a transverse wave, which propagates at the third critical angle, become notice- able; however, this is not considered here. A Rayleigh run-round wave can easily be observed using an SO-2 specimen. Weak pulses of run-round waves and slide-off waves are noticeable following the signal reflected from a hole 6 mm in diameter. The nonmonotonic behavior of the amplitude of reflected transverse waves is explained by the interference of the direct reflected wave and the first run-round and slide-off waves for a cylinder of small diameter (less than 6 mm). None of this was known in 1972 when I decided to check experimentally how the reflection amplitude from a cylindrical hole varied. The issue was that the experimental points reported in the paper by Golubev were spaced rarely and did not conclusively confirm a nonmonotonic behavior. Moreover, Golubev worked with long-duration pulses and used face-par- allel-cut quartz to emit and receive transverse waves. I ordered specimens from aluminum with side holes 3-6 mm in diameter with a step of 0.1-0.2 mm in the assumed nonmonotonic zone. Presumably, it was impossible to miss a nonmonotonic behavior if such a small step was used. Additionally, two holes were drilled with diameters much larger than the wavelength (9 and 12 mm) for matching the curve B = 0.5 that described the variation in the