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{{PSM_Infobox}}
Refraction sound waves
__FORCETOC__

==Refraction of sound waves – Law of refraction==

Refraction is basically defined as the discontinuous change in direction of energy transport at the [[Phase Boundary Surface|interface]] between two media into the adjacent medium. Energy transport can occur in the form of electromagnetic waves (e.g. light, heat) and sound waves. In an unlimited or semi-limited medium, these waves can occur as plane waves or spherical waves, depending on the source mechanism ('''Fig. 1'''), whereby both wave types are volume waves whose wavelength is small in comparison to the propagation medium.

[[File:Refraction Sound Waves - Fig1.jpg|450px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px"|Types of waves in an infinite medium a) spherical waves and b) plane waves
|}

==Types of sound waves==

Sound waves can occur in two forms in volume (volume waves): as longitudinal waves (pressure waves) and as transverse waves (shear waves), in which the volume elements oscillate in or transverse to the direction of propagation of the wave. As a result, both types of waves have different propagation speeds ('''Fig. 2'''). Longitudinal waves occur in solid, liquid and gaseous media, while transverse waves only occur in solid [[Material & Werkstoff|materials]] that can transmit shear forces.

In contrast to electromagnetic or water waves (surface waves or Rayleigh waves), longitudinal waves are partially converted into transverse waves at medial [[Phase Boundary Surface|interfaces]] and vice versa ('''Fig. 3'''). The degree to which the incident wave is refracted depends on the acoustic properties of the two media and the angle of incidence ''α''. The types of waves listed differ in their direction of deflection and their propagation velocity ''c''L or ''c''T, respectively.

[[File:Refraction Sound Waves - Fig2.jpg|450px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px"|Volume waves and their propagation velocity a) Longitudinal wave and b) Transverse wave
|}

==The generalised law of refraction==

Due to the wave propagation behaviour of sound waves, a generalised law of refraction ('''Eq. 1''') applies to all waves, which is shown schematically in '''Fig. 3''':

{|
|-
|width="20px"|
|width="600px"|<math>\frac{\sin \alpha _{i}}{c_{i}}=\frac{\sin \alpha _{k}}{c_{k}}</math>
|(1)
|}

[[File:Refraction Sound Waves - Fig3.jpg|400px]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px"|Schematic presentation of the generalised law of refraction
|}

The indices ''i'' and ''k'' denote the sound rays (incident ray and refracted ray) at the interfaces of the media, but also the longitudinal (LW) and transverse (QW) waves of the respective medium.

==The law of reflection for sound waves==

'''Equation (1)''' can also be used to derive the law of reflection and determine the critical angle of total reflection (see: [[Ultrasonic Waves Reflection|ultrasonic waves reflection]]). When sound waves strike flat [[Phase Boundary Surface|interfaces]] between two solid media at an angle, wave conversion occurs as a result of [[Ultrasonic Waves Reflection|reflection]], refraction and splitting of the wave, with the specific characteristics being determined by the reflection (R) and transmission (T) factors between the media ('''Fig. 4''') (see: [[Transmission Sound Waves|transmission sound waves]]). If medium 1 is a shear stress-free substance, such as water or air, then no transverse waves (TW) are split off. In this case, reflection ('''Eq. 2''') and refraction ('''Eq. 3''') of the longitudinal wave (LW) occur in medium 1 and medium 2, respectively.

{|
|-
|width="20px"|
|width="500px"| <math>\frac{\sin \alpha _{0}}{\sin \alpha _{D}}=\frac{c_{L1}}{c_{L1}}=1</math>
|(2)
|}

{|
|-
|width="20px"|
|width="500px"| <math>\frac{\sin \alpha _{0}}{\sin \alpha _{D}}=\frac{c_{L1}}{c_{L2}}</math>
|(3)
|}

In medium 2 ('''Eq. 4''') and medium 1 ('''Eq. 5'''), a transverse wave (TW) is split off in each case, which has a different propagation velocity than the longitudinal wave (LW) (frequency dispersion). Both refraction and [[Ultrasonic Waves Reflection|reflection]] depend on the angle of incidence of the ultrasound and the refractive index ([[Refraction Index|refraction index]]) as well as the characteristic acoustic impedance ''W'' of the media.

{|
|-
|width="20px"|
|width="500px"| <math>\frac{\sin \alpha _{D}}{\sin \beta _{D}}=\frac{c_{L2}}{c_{T2}}</math>
|(4)
|}

{|
|-
|width="20px"|
|width="500px"| <math>\frac{\sin \alpha _{R}}{\sin \beta _{R}}=\frac{c_{L1}}{c_{T1}}</math>
|(5)
|}

[[File:Refraction Sound Waves - Fig4.jpg|350px]]
{|
|- valign="top"
|width="50px"|'''Fig. 4''':
|width="600px"|Reflection and refraction of ultrasound at a flat interface
|}

In [[Ultrasound Testing|ultrasonic testing technology]], the law of refraction is applied in practice primarily in defectoscopy, particularly when using angle beam sensors for weld seam testing with the [[Pulse-Echo Ultrasonic Technique|pulse-echo method]] or the [[Ultrasonic Time-of-Flight Diffraction (TOFD) Technique|time-of-flight diffraction (TOFD) method]].

==See also==

* [[Absorption Sound Waves|Absorption sound waves]]
* [[Ultrasonic Waves Reflection|Reflection sound waves]]
* [[Transmission Sound Waves|Transmission sound waves]]
* [[Ultrasound Testing|Ultrasound testing]]
* [[Sound Emission|Sound emission]]
* [[Sound Emission Experimental Conditions|Sound emission experimental conditions]]
* [[Sound Emission Analysis|Sound emission analysis]]

==References==

* Matthies, K. u. a.: Dickenmessung mit Ultraschall. DVS Media Publishing, Berlin (1998) 2nd Edition (ISBN 3-87155-940-7; see [[AMK-Library]] under M 44)
* Šutilov, V. A.: Physik des Ultraschalls. Springer, Berlin (2013) (ISBN 978-3-70918-750-0) p. 155 ff.
* Deutsch, M., Platte, V., Vogt, M.: Ultraschallprüfung. Grundlagen und industrielle Anwendungen. Springer, Berlin (1997) (ISBN 3-540-62072-9; see [[AMK-Library]] under M 45)
* Steeb, S. (Eds.): Zerstörungsfreie Werkstück- und Werkstoffprüfung. Expert Publishing, Ehningen (2019), 5th Edition (ISBN 978-3-8169-3261-1)

[[Category:Acoustic Test Methods_Ultrasonics]]

Refraction Sound Waves - Revision history