How do sound waves reflect at or pass through interfaces?
In this article:
- NDT Relies on Sound Wave Interaction: How sound waves interact at material boundaries (interfaces) is crucial for NDT, as waves reflect and transmit based on material properties.
- Acoustic Impedance Drives Reflection/Transmission: The reflection (R) and transmission (D) factors depend primarily on the acoustic impedances (Z1, Z2) of the two media.
- Oblique Incidence Causes Refraction & Mode Conversion: Sound waves striking an interface at an angle refract (change direction per Snell's Law) and can undergo mode conversion in solids, generating both longitudinal and shear waves.
- Critical Angles Limit Wave Types: Increasing the angle of incidence leads to critical angles where certain wave types (longitudinal or shear) stop transmitting, leaving only other types or surface waves.
- Waygate Technologies Unlocking Precision in Ultrasonic Wave Interaction: Waygate Technologies provides ultrasonic testing equipment (equipment, probes, software) to precisely control and interpret sound wave behaviour at interfaces, aiding in superior defect detection and material characterization.
Understanding how sound waves behave when they encounter a boundary between two different materials is fundamental to many applications, particularly in non-destructive testing (NDT) using ultrasound. These boundaries, or interfaces, cause a sound wave to either bounce back (reflect) or continue through (transmit), and the proportion of each is determined by the material properties involved. Let's explore the physics behind these interactions.
They exist for sound propagation where two media with different elastic properties join. If a sound wave with a plane wave front hits an interface between otherwise unbounded media, it is partly reflected as a plane wave and partly transmitted (fig. 28). The ratio between the sound pressure of the reflected wave pr and the pressure of the incoming wave pi is the reflection factor R:
The ratio of the passing wave pt to the incident wave pi is the through-transmission factor D:
Decisive for the magnitude of R and D are the acoustic impedances Z1 = ρ1c1, and Z2 = ρ2c2 of both media, equations (26) and (27).
Between equations (26) and (27) there is the relationship (28):
(28) D=1+R
The pressure which passes through the interface and the reflected pres- sure amplitude by no means add up to 1 i. e. their sum is not the pressure of the incident wave. This relationship only applies to the energy.
If the arrangement of the Interfaces is reversed, which is forcibly the case with the echo method, one obtains (26'):
The amount of the reflected amplitude remains the same only the phase is reversed.
As the factors R and D or R' and D' represent ratios they can also be given as dB-values. This should be represented by the example of the sound transfer from steel into water:
The magnitude of the reflected amplitude is thus only 0,6 dB lower than that of the incident amplitude (almost ideal reflection).
The wave which passes from steel into water has a sound pressure which is approx. 24 dB below the sound pressure of the incident wave.
The Phenomenon of Refraction and Mode Conversion
If the sound wave strikes the interface at an angle, then the reflected waves and the waves which pass through the Interface are more complicated to calculate. But another important effect with inclined impingement must be dealt with: the refraction. When passing through the interface waves changes the direction of propagation according to the Snell’s refraction law (fig. 29):
In solid bodies there are also wave mode conversions when the waves are refracted at interfaces. An incident longitudinal wave in fig. 29 generates, in medium 2, a refracted longitudinal wave and also a refracted transverse or shear wave. Here the refraction law (32) applies:
If sinβlong = 1 then the limiting angle is α’, also known as the first critical angle (fig. 30), equation (33):
For incidence angles α > α‘ there is no longer any refracted longitudinal wave in medium 2, there are only shear waves. If sinβshear = 1 then there is a second limiting angle α" (second critical angle, fig. 31), equation (34):
For an incidence angles greater than α" there is neither a longitudinal nor a shear wave in medium 2, there are surface waves and they only exist at the interface.
With the refraction law only the direction of propagation of the refracted wave can be calculated but not however its amplitude. Apart from that the refraction law does not make it clear that transverse waves are always linear polarised after having been reflected or refracted.
An additional complication in the practical test is that there are never unlimited plane wave fronts: the sound beam is limited and the wave fronts are not plane. Nevertheless, the reflection at interfaces is the most important phenomenon in the ultrasonic testing of materials. With angle beam probes (fig. 11) one uses the refraction with an incidence angle greater than α' and smaller than α" in order to generate only one linear polarized shear waves in the material being tested.
The behaviour of the reflected wave in the vicinity of the limiting angles can be taken advantage of in order to evaluate the elastic properties in the material (critical angle reflectivity).
Conclusion
The reflection and transmission of sound waves at interfaces are complex but predictable phenomena governed by fundamental physical laws. From the simple reflection of a normally incident wave to the intricate process of refraction and mode conversion at oblique angles, understanding these behaviours is paramount for anyone working with acoustics or ultrasonic technology.
The ability to manipulate and interpret these wave interactions allows for powerful applications in material characterization, defect detection, and a wide array of scientific and industrial fields. Mastering these concepts is a key step towards effectively harnessing the power of sound waves.
Information on the real refraction at interfaces and on the reflection with critical angle can be found in the following publications
[11]. A. Nickerson: A new view of the elastic theory upon which ultra- sonic testing is based (Int. J. Non-Destr. Testing (1971) no 2,
81-98
[12] F. L. Becker, R. L. Richardson: Ultra- sonic critical angle reflectivity Research Techniques in Non-de- structive Testing vol. 2 (ed. R. S. Sharpe) Académie Press, London (1970), chapter 4