THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

12.6 Coincidence Effect and Critical Frequency 287Figure 12.3. The coincidence effect affected by bending waves.orsin θ ∗ = λ λ b.With the asterisk indicating the occurrence of coincidence, θ ∗ denotes the coincidenceangle. Under such circumstances, the sound pressure on the surface of thepanel falls into phase with bending displacement. This results in a highly efficienttransfer of acoustic energy from the airborne sound waves on the source side ofthe panel to bending waves in the panel, and thence to airborne sound waves inthe receiving room on the other side of the panel. This is a highly undesirablesituation if the panel is meant to prevent the transmission of sound from one roomto another as a noise control measure.Figure 12.4 shows an idealized plot of transmission loss for a panel as a functionof frequency, with stiffness-controlled, resonance-controlled, mass-controlled, andcoincidence-controlled regions. The transmission loss curve drops considerably inthe region beyond the critical frequency owing to the coincidence effect.From Equation (12.15) it can be deduced that the coincidence effect cannotoccur if the wavelength λ of the airborne sound is greater than the bending modewavelength λ b in the panel. The minimum coincidence frequency, or the criticalfrequency, exists at the critical airborne sound wavelengthλ = λ ∗ = λ b