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At one frequency, called the coincidence frequency, the mass and bending impedance terms are equal and, since they have opposite signs, the composite impedance is zero. Figure 9.7 illustrates the crossover point for this condition.

Coincidence can be understood by realizing that the velocity of bending waves in a panel is a function of frequency. At the coincidence frequency, the bending wave velocity is the same as the trace velocity of the airborne sound moving along the panel. Since the pressure maxima and minima are spatially matched, as in Fig. 9.8, energy is easily transmitted from the air into the panel and vice versa. The frequency at which coincidence occurs varies with the angle of incidence and is obtained by setting Eq. 9.26 to zero c2 I-

Figure 9.7 Imaginary Part of the Thin Panel Impedance (Sharp, 1973)

The imaginary part of the transmission impedance of a thin panel for grazing incidence (6 = n/ 2) showing the effect of coincidence.

Figure 9.7 Imaginary Part of the Thin Panel Impedance (Sharp, 1973)

The imaginary part of the transmission impedance of a thin panel for grazing incidence (6 = n/ 2) showing the effect of coincidence.

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