A Terminating Resonator

Suppose a guitar bridge couples an ideal vibrating string to a single resonance, as depicted schematically in Fig.9.5. This is often an accurate model of an acoustic bridge impedance in a narrow frequency range, especially at low frequencies where the resonances are well separated. Then, as developed in Chapter 7, the driving-point impedance seen by the string at the bridge is

$$R_b(s) \eqsp ms + \mu + {k/s}.$$

That is, the driving-point impedance is the series combination of a mass $m$ , spring $k$ , and dashpot $\mu$ (§7.2). More general bridge impedances can be modeled as a sum of such terms. Since the bridge is passive, $R_b(s)$ is positive real (§C.11.2).

Figure 9.5: Ideal vibrating string terminated by a second-order driving-point impedance consisting of a mass $m$ , spring $k$ , and dashpot $\mu$ .