BASICS OF ACOUSTICS:1.6 Relationship between the processes of reflection, refraction and transformation to the angle of incidence of the longitudinal waves

The laws of the wave media boundary passing define the course of the processes of waves propagation from the transducer into the controlled object and back. Fig. 2.6 schematically shows an inclined transducer installed on the controlled object. Acoustic wave of a longitudinal type arises in the converter prism, and falls on the boundary to the object the control at a certain angle to the normal.

Схема прохождения волны из призмы преобразователя в объект контроля

Fig. 2.6 – The wave passage from prism of the converter to the controlled object Scheme

Depending on the angle of incidence of the longitudinal waves only, penetrate the test object, longitudinal and transverse, or only transverse surface wave. If the fall of the longitudinal wave at the boundary between the media occurs through the normal (Fig. 2.7, a) β0 = 0º transverse waves do not occur, and the reflected and transmitted waves are also subject to the normal. In each medium, two waves propagate, and the angles of longitudinal waves are greater than the angles of shear.

The first critical angle (Fig. 2.7, c) is called the minimum angle of incidence of the longitudinal waves at which the longitudinal wave does not penetrate into the second medium. At angles of incidence close to the first critical one, heterogeneous head-longitudinal wave arises at the boundary between media, which quickly fades, re-radiating side transverse waves. For Plexiglas-steel border the first critical angle is β1kr = 27º.

If a longitudinal wave is incident at an angle to the normal greater than the first but less than the second critical angle only shear wave penetrates into the second medium. This allows to control the object only by transverse waves. The second critical angle (Fig. 2.7, d) is called the minimum angle of incidence of the longitudinal waves at which the shear wave does not penetrate into the second medium. At angles of incidence close to the second critical for distributed heterogeneous boundary-head the shear wave that quickly fades. If the angle of incidence close to the second critical angle, there is inhomogeneous head-shear wave at the interface, which quickly fades. For the boundaries Plexiglas-steel the second critical angle is β2kr = 55º. At angles greater than the second critical value (Fig. 2.7, e) volume waves (longitudinal and transverse) do not penetrate into the second medium.

a)Схема падения продольной волны на границу под углом 06 b)Схема падения продольной волны на границу под углом 05 c)Схема падения продольной волны на границу под углом 04

d)Схема падения продольной волны на границу под углом 03 e) Схема падения продольной волны на границу под углом 02f) Схема падения продольной волны на границу под углом 01

Fig. 2.7 – Scheme of incidence of the longitudinal wave on the boundary at an angle β0 illustrates the first and second critical angles.

Surface wave occurs at the boundary of the second medium upon impact by the longitudinal wave at angle β0 ≈ 59º (Fig. 2.8).

Схема падения продольной волны на границу под углом 07

Fig. 2.8 – Scheme of fall of longitudinal wave on the boundary at β0 angle, shows surface wave excitation

Let us consider the fall of the transverse wave at the boundary between two media, for example, steel to air. When the angle of incidence is less than the third critical β0 <β3kr (Figure 2.9 a.) two waves: longitudinal and transverse, are reflected from the boundaries.

The third critical angle (Fig. 2.9, b) is such angle of incidence of a transverse wave, at which the reflected longitudinal wave disappears. At those angles that are close to the third critical angle, along the boundary distributes inhomogeneous head-longitudinal wave (similar to the first critical angle), which quickly fades, re-radiating side transverse waves. For steel the third critical angle is β3kr = 34º. At angles greater than the third critical angle β0> β3kr only shear wave reflects from the boundary (Fig. 2.9, c).

In the considered above examples of reflection, refraction, and the transformation only one central beam is taken. In practice, on the boundary between medias a bunch of beams falls. For flat front waves all the rays will interact with the boundary in the same manner, so the described above processes remains valid.

 

 

Fig. 2.9 – scheme of the fall of the transverse wave at the boundary at an angle β0 illustrates a third critical angle