Transmission Sound Waves

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Transmission sound waves

Fundamentals of transmission

Alongside reflection and absorption, the transmission of sound waves is a phenomenon that occurs at the external or internal boundary surfaces of components or test pieces. In ultrasonic testing technology, penetration testing is often also referred to as ultrasonic transmission technique.

Transmission is essentially a parameter for electromagnetic waves (e.g. sound waves) that describes the permeability of a medium or material and its interfaces for these waves. The interface itself is formed by adjacent layers (e.g. metal or air with water) that have different characteristic sound impedances or sound impedances W or Z.

An incident sound wave is partially reflected at an interface and partially transmitted or transferred to the neighbouring layer (cross-coupling). The prerequisite for this is that both neighbouring layers have different sound impedances W, whereby it is not the absolute value but the difference in sound impedances ΔW that is decisive.

Sound wave resistance or characteristic acoustic impedance

The sound wave resistance or characteristic impedance of materials, calculated as the product of density ρ and sound velocity c with Z or W = ρ c, is particularly important for the reflection and transmission behaviour of sound waves. This parameter describes the typical elastic properties of materials, whereby materials with a high W value are described as sound-hard (Fe, Cu, Ni) and those with low W values (PMMA, Al, H2O) as sound-soft [1–4]. If the absorption of the ultrasonic wave is neglected, then depending on the ratio of W₁ (sound-hard) to W₂ (sound-soft) at the interface, only transmission and reflection occur (Fig. 1).

Fig. 1:

Reflection and transmission at the interface between two media a) and between the ultrasonic sensor and the workpiece surface b) with perpendicular sound incidence [7]

The transmission part is greater the smaller the differences between the sound impedances W₁ and W₂. However, if the difference between W₁ and W₂ is very large, as is the case with vacuum or air as the second medium, for example, then a high to total part of the incident sound wave is reflected and no transmission occurs. This effect has a major influence on the detectability of defects in ultrasound testing, both in the ultrasonic transmission technique and pulse-echo ultrasonic technique.

Transmission degree and transmission factor

In general, the transmission degree T or τ is defined as the quotient between the sound intensity before and after the interface (Eq. 1). It is therefore a parameter for the transmitted intensity I and lies in the range between 0 and 1.

$\tau ={\frac {I}{I_{1}}}$

(1)

The transmission degree of acoustic waves depends significantly on the thickness d of the test piece, the wavelength λ and the frequency f, so that Eq. (2) actually applies. The frequency-dependent relationship is used, for example, in building acoustics to describe the acoustic insulation capacity of components, for which the logarithmic sound insulation index R is used (Eq. 3).

τ = τ(λ) or τ(f)

(2)

$R=10\lg \left({\frac {I_{0}}{I}}\right)$

(3)

Analogous to the reflection factor R, a transmission factor T can be specified for sound waves, which indicates how large the transmitted or passed portion P_D is (Fig. 1a), whereby this parameter refers to the amplitude of the sound waves rather than their intensity. This parameter D or T is also significantly dependent on the difference between the sound impedances W₁ and W₂ (Eq. 4) [5, 7].

$T={\frac {2W_{2}}{W_{1}+W_{2}}}$

(4)

When longitudinal waves are transmitted using vertical sensors, a high part of the sound waves is transmitted at the interface between the sensor and the test piece if the surface is very smooth and flat and a suitable coupling agent (water, coupling gel) is used (Fig. 1b). In the case of the immersion bath and squirter techniques or when using air-ultrasound, the coupling problem does not occur. When sound waves are incident perpendicular to flat interfaces, no wave conversion occurs and, for identical media (W₁ = W₂), R = 0 and T or D = 1, i.e. there is unimpeded sound transmission into medium 2. If there is no absorption in the medium, the intensity or amplitude of the incident wave is identical to that of the outgoing sound wave.

Fig. 2:

Reflection and transmission at the interface between two media a) and between ultrasonic sensor and specimen surface b) with oblique sound incidence [7]

If the ultrasound enters the interface at an angle (Fig. 2), mode conversion or wave conversion, reflection, transmission and refraction will occur in conjunction with frequency dispersion. Mode conversion is very important for some ultrasonic testing techniques, such as ultrasonic angle beam sensors. In this case, a transverse wave is additionally generated for both the reflected and transmitted waves. In the case of the angle sensor, depending on the difference in acoustic impedances and the angle of incidence, the longitudinal wave is totally reflected in medium 2 and the reflected transverse and longitudinal waves are attenuated in the sensor by an intermediate layer. In this case, the transmission factor T is calculated according to Eq. (5) as

$T={\frac {P_{D}}{P_{0}}}$ with $T=R+1$.

(5)

Application in defectoscopy

In ultrasonic defectoscopy, defects or discontinuities in the material are more easily detectable the greater the differences in sound waves (echo detectability) are (e.g. steel − air: R >> - 1). Thin layers of air can prevent the transmission of sound waves into the material even with plane-parallel air gaps of 10 nm between the test head (steel) and a rough surface (air) at a test frequency of 1 MHz due to the large differences in W. In transmission testing, the detection of defects (voids, inclusions, delaminations, doublings or cracks) or discontinuities is based on the transmission of the pulsed or continuous transmission pulse to the receiver sensor, therefore a transmitter and receiver sensor are always required. The measured amplitude pattern indicates the presence of defects and their spatial extent. The ultrasonic transmission technique can be used in standard, transmitter (S)-receiver (E) sensor and angle testing techniques.

Fig. 3:

Ultrasonic transmission testing method on a test piece with a defect at a perpendicular sound incidence angle [7]

See also

• Transmission light
• Non-desdructive polymer testing
• Velocity
• Ultrasonic direct coupling
• Ultrasonic birefrigence

References

[1]	Krautkrämer, J., Krautkrämer, H.: Ultrasonic Testing of Materials. Springer, Berlin (1990) 4th Edition, (ISBN 978-3-540-51231-8)
[2]	Lerch, R., Sessler, G., Wolf, D.: Technische Akustik – Grundlagen und Anwendung. Springer, Berlin (2009) (ISBN 978-3-540-49833-9)
[3]	Möser, M.: Technische Akustik. Springer, Berlin (2015) (ISBN 978-3-662-47704-5)
[4]	Šutilov, V. A.: Physik des Ultraschalls. Springer, Berlin (2013) (ISBN 978-3-70918-750-0) S. 155 ff.
[5]	Deutsch, V., Platte, M., Vogt, M.: Ultraschallprüfung. Grundlagen und industrielle Anwendungen. Springer, Berlin (2013) p. 33 (ISBN 978-3-642-63864-0)
[6]	Busse, G.: Non-desdructive Polymer Testing. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 431–495 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-805-5; see AMK-Library under A 22)
[7]	Bierögel, C.: Lecture Notes: Materials Diagnostics – Hybrid Testing Methods. Vienna University of Technology (2015)