For the analysis of materials, ZVUK instruments utilize the correlation relationship existing between the frequencies of oscillations of the material itself and its physical-mechanical functional characteristics. The frequency of inherent oscillations is affected by the input material characteristics, and also by the hardness of individual components and by the whole product, and by porosity and other physical material parameters. Generally, it is possible to define the correlation between the material inherent oscillations and the structural constants and dimensions by this equation:
| where: | fi - frequency of inherent oscillations that corresponds to the selected "i" frequency types |
| Fi - shape coefficient that is dependent on the shape of a specific material element, its dimensions, type of selected frequency, and on the Poisson number | |
| Cl - propagation velocity of sonic waves through the measured material. The velocity of the measured material emanates from the equation and represents the velocity of longitudinal propagation of the sonic waves on the axis of the rod infinite in its length In the equation, the "E" is the value of E-Module elasticity (Yang's Elasticity Module), and ρ is the value of the bulk specific gravity of the measured material element |
The following schematic figure shows the characteristics of oscillations within individual material elements during an evaluation of various frequency types. The dashed lines represent the nodal lines that remain inactive with the specific frequency type.
f1 and f2 frequencies correspond to the in-plane deflection of the disc perpendicular to the disc axis with two nodal diameters and nodal circular rings (see the dots marked "a" and "b" on the figure below).

"Plus" and "Minus" represents the motion of material element components in the perpendicular plane in the direction upward and downward. The motion direction of these components is changed halfway through each period.
fd frequency corresponds to the direction of oscillation movements inside the disc diagonally towards its diameter, with two nodal plains (see the dot marked "c" on the figure above). The movements of the material element towards the hole in the disc within the various parts of the period are marked by a dashed line pattern.
ftorz frequency represents the torque frequency of oscillations inside the rod with the nodal plain in the centre of the rod (see the dot "d" on the figure above); the direction of torque is marked by the arrow-tips.
fpl frequency corresponds to the longitudinal oscillations of the rod with two nodal plains (see the dot marked "e"); the dashed lines represent the arithmetic averages of oscillations for each half of the period. The "fpl", another type of longitudinal oscillation (see the dot marked "f" in the figure above), corresponds to the rod oscillations with one nodal plain that crosses the centre of the rod. The directions of oscillations are marked by the arrow-tips.