#### A Two-Resonance Guitar Bridge

Now let's consider a two-resonance guitar bridge, as shown in Fig. 9.6.

Like all mechanical systems that don't ``slide away'' in response to a
constant applied input force, the bridge must ``look like a spring''
at zero frequency. Similarly, it is typical for systems to ``look
like a mass'' at very high frequencies, because the driving-point
typically has mass (unless the driver is spring-coupled by what seems
to be massless spring). This implies the driving point admittance
should have a zero at dc and a pole at infinity. If we neglect
losses, as frequency increases up from zero, the first thing we
encounter in the admittance is a pole (a ``resonance'' frequency at
which energy is readily accepted by the bridge from the strings). As
we pass the admittance peak going up in frequency, the phase switches
around from being near (``spring like'') to being closer to
(``mass like''). (Recall the *graphical method* for
calculating the *phase response* of a linear system
[449].) Below the first resonance, we may say that the system
is *stiffness controlled* (admittance phase
),
while above the first resonance, we say it is *mass controlled*
(admittance phase
). This qualitative description is
typical of any lightly damped, linear, dynamic system. As we proceed
up the axis, we'll next encounter a near-zero, or
``anti-resonance,'' above which the system again appears ``stiffness
controlled,'' or spring-like, and so on in alternation to infinity.
The strict alternation of poles and zeros near the axis is
required by the *positive real* property of all passive
admittances (§C.11.2).

**Next Section:**

Measured Guitar-Bridge Admittance

**Previous Section:**

Digitizing Bridge Reflectance