A Two-Resonance Guitar Bridge
Now let's consider a two-resonance guitar bridge, as shown in Fig. 9.6.
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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