Coincidence frequency

Flexural wave in a plate (orange) excited by a sound wave (blue wave fronts). The shorter arrow shows the direction of incidence (angle θ) and the wavelength λ in air. The longer arrow shows the wavelength λ / sin θ of the flexural wave. There is coincidence when the flexural wave is faster than the speed of sound by the same factor 1 / sin θ.

In acoustics, coincidence or track adaptation is the correspondence between the frequency- dependent phase velocity of flexural waves in flat components and the frequency-independent velocity of the trace of the air wave on the component. The coincidence frequency at which this occurs depends on the speed of the track, i.e. the intersection lines of the wave fronts with the surface, on the angle of incidence. For grazing incidence, the coincidence frequency tends towards the coincidence limit frequency ${\displaystyle f_{g}.}$

The coincidence causes a break in the sound insulation of the component.

The following applies to flat or at least developable components with properties that are homogeneous over the surface

${\displaystyle f_{g}={\frac {c_{l}^{2}}{2\pi }}{\sqrt {\frac {m''}{B'}}}}$

With

• ${\displaystyle c_{l}}$: Speed ​​of sound in air
• ${\displaystyle m''}$: mass per unit area of the material
• ${\displaystyle B'}$: bending stiffness of the material related to the width

For non-layered, that is homogeneous across the thickness of material applies with ${\displaystyle B'=E\cdot I'}$

• ${\displaystyle E}$: Young's modulus
• ${\displaystyle I'=d^{3}}$: area moment of inertia related to the width of the cross-section .

When it comes to sound insulation, it is important to dimension a component so that the coincidence frequency is in the inaudible range, e.g. B. by increasing or decreasing the mass or the flexural rigidity (up to 100 Hz rigid, over 3125 Hz flexible component).

Multi-shell components can have several coincidence frequencies. Soundproof glazing or soundproof drywall walls, for example, have glass panes of different thicknesses or cladding in order to prevent an extreme breakdown in sound insulation through the frequency offset of the coincidence frequencies.

Web links

• Significance of the coincidence frequency for the sound insulation of components