Refraction Sound Waves

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Refraction sound waves

Refraction of sound waves – Law of refraction

Refraction is basically defined as the discontinuous change in direction of energy transport at the 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.

Fig. 1:

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 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 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.

Fig. 2:

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:

{\frac {\sin \alpha _{i}}{c_{i}}}={\frac {\sin \alpha _{k}}{c_{k}}}

(1)

Fig. 3:

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). When sound waves strike flat interfaces between two solid media at an angle, wave conversion occurs as a result of 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). 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.

{\frac {\sin \alpha _{0}}{\sin \alpha _{D}}}={\frac {c_{L1}}{c_{L1}}}=1

(2)

{\frac {\sin \alpha _{0}}{\sin \alpha _{D}}}={\frac {c_{L1}}{c_{L2}}}

(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 reflection depend on the angle of incidence of the ultrasound and the refractive index (refraction index) as well as the characteristic acoustic impedance W of the media.

{\frac {\sin \alpha _{D}}{\sin \beta _{D}}}={\frac {c_{L2}}{c_{T2}}}

(4)

{\frac {\sin \alpha _{R}}{\sin \beta _{R}}}={\frac {c_{L1}}{c_{T1}}}

(5)

Fig. 4:

Reflection and refraction of ultrasound at a flat interface

In 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 method or the time-of-flight diffraction (TOFD) method.

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)

Refraction of sound waves – Law of refraction

Types of sound waves

The generalised law of refraction

The law of reflection for sound waves

See also

References