# Coincidence

The sound radiation efficiency of a plate is dependant upon the coupling of sound waves in the air and flexural waves (vibration) in the plate. Optimum efficiency (maximum energy transfer from vibration to sound or visa versa) is achieved when the plate is vibrated such that the wavelength of flexural waves in the plate is equal to the wavelength of acoustic waves in the air (alternatively the flexural wave velocity in the plate is equal to the velocity of acoustic waves in the air). This is more commonly known as the coincidence or critical frequency of radiation fc.
 where fc = coincidence frequency [Hz] c = speed of sound in air [ms-1] d = thickness of panel [m] ρ = density of panel [kgm-3] Y = Young's modulus of panel [Nm-2]
For all frequencies above fc there exists an angle of incidence such that the projection of the incident wave coincides with the flexural wave.
where
= wavelength in panel [m]
λ = wavelength in air [m]
θ = angle of incidence with respect to normal [rad]

Subjects: Noise & Vibration