Acoustic Properties

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Acoustic properties

Fundamentals

The acoustic properties are essentially represented by the material values sound velocity and acoustic damping. They are closely linked to the mechanical [[Material Parameter|material parameters] modulus of elasticity (abbreviated to modulus E) and Poisson's ratio, as well as toughness. The relationship between the sound velocity v, the modulus of elasticity M and the Poisson's ratio µ is shown in the following equation:

$v={\sqrt {\frac {M}{\rho }}}\cdot f(\mu )$.

(1)

Here, M is the modulus, which can be the elastic modulus, shear modulus, or compression modulus, depending on the type of excitation, and ρ is the mass density (see: density) of the material. In the case of longitudinal waves (i.e., wave propagation and particle vibrations are parallel), Eq. (1) becomes

$v={\sqrt {{\frac {E}{\rho }}\cdot {\frac {1-\mu }{(1+\mu )(1-2\mu )}}}}$.

(2)

Acoustic damping and acoustic damping coefficient

Due to the internal friction of the volume elements when the wave passes through the medium, acoustic damping shows an exponential dependence of the sound intensity:

$I(x)=I_{0}\ e^{-2\alpha x}$.

(3)

The factor 2 arises from the double sound path in the pulse-echo ultrasonic method. The factor α in the exponent of Eq. (3) is the acoustic damping coefficient; it has the dimension 1/m and thus represents a material-specific characteristic value, which, however, depends on the measurement frequency:

$\alpha =\alpha (\omega )\!$.

(4)

Temperature dependence of acoustic properties

Plastics in particular have acoustic and mechanical properties that are highly dependent on temperature, which influences the viscoelastic behaviour and damping (Eq. 5) of these materials in particular.

$\alpha ={\frac {4\eta (T)}{3\rho c^{3}}}\omega ^{2}$.

(5)

The following Table lists some sound velocities and specific damping values for selected materials.

material	sound velocity (long.) vs (m s-1)	specific damping V (dB mm-1)
steel	5,900	0.25
aluminium	6,400	0.13
brass	4,300	0.15
synthetic rubber	1,460	4.12
PMMA	2,540	0.31
PS	2,350	2.07
PVC	2,300	1.85
PA 6	2,570	2.38
PP	2,550	2.26
PE	1,800	2.26
Derakane 411	2,400	0.55
Derakane 470	2,700	0.33
Derakane 411 (36 M.-% GF)	2,510	0.70
Derakane 411 (70 M.-% GF)	3,050	0.50

See also

• Acoustic emission
• Sound velocity
• Non-destructive testing (NDT)
• Sound testing

References

• Šutilov, V. A.: Physik des Ultraschalls. Akademie Verlag, Berlin (1984) (ISBN 978-3-7091-8750-0)
• Šutilov, V. A.; Hauptmann, P.: Physik des Ultraschalls. Springer Wien (2012) (ISBN 978-3-7091-8751-7)
• Kuttruff, H.: Akustik – Eine Einführung. S. Hirzel Verlag, Stuttgart Leipzig (2004)(ISBN 978-3-7776-1244-7)
• Koschkin, N. I., Schirkewitsch, M. G.: Elementare Physik. Akademie Verlag, Berlin (1987) (ISBN 978-3-4461-4893-2)