I haven't quite been able to go through the more than 100MB of PDF pages of the most detailed book ever written about everything guitar... but it is bound to be in there... It is also complex reading as the writer uses math as if there is no tomorrow. Below a few pages I copied and pasted to not wet your appetite
7.9 The Wood Determines the Sound?
Mahogany! Maple! Rosewood! Men oft believe, if only they hear wordy pother, that there
must surely be in it some thought or other [Goethe]. And the usual thinking is: “the electric
guitar is a musical instrument made of wood. In all musical instruments made of wood, the
wood determines the sound. The more noble the wood, the more noble the sound.” Goethe’s
witch’s kitchen – a suitable location for deception and magic – holds more such articles of
faith, but let us keep some distance from alchemy, and give physics the priority here: how
does the body of the guitar vibrate, and in what way will the vibration of this body influence
the sound? In the material-science course, every luthier learns about different tonewoods and
their sound-determining material-parameters: “the denser the wood, the more brilliant, treblerich the sound; the higher the stiffness, the longer the sustain (P. Day).” As if that were selfevident, this statement and similar ones are based on the assumption that the findings that are
valid for violins and acoustic guitars apply to electric guitars, as well. If we now add that
board of experts who listen to an electric guitar first of all without amplification, we quickly
arrive at a conglomerate of teachings that, between them, could not be more contradictory. All
the while two simple principles would really help us:
1) Compared to the acoustic guitar, the electric guitar functions very differently. Findings
derived from the one type of guitar may not be sight-unseen applied to the other type.
2) There is a connection between the vibration of the strings and the (airborne) sound directly
radiated by the electrical guitar. There is also a connection between the vibration of the strings
and the sound radiated by the loudspeaker – but this latter connection is very different from
the former.
The fundamental differences between acoustic and electric guitar become evident when we
look at the energy flow: being plucked, the guitar string receives energy that is in part
converted in to sound energy, and in part into caloric energy (heat). A – not untypical –
excitation energy of E = 3.6 mWs corresponds to the billionth part of one kilowatt-hour
(kWh); that’s really very little compared to household appliances but still enough to generate
a sound that is clearly heard. With an acoustic guitar, this energy can generate an SPL of
about 94 dB at the ear of the player; a Les Paul only reaches about 64 dB. A level difference
of 30 dB translate onto a power relationship of 1000 to 1, which confirms quantitatively what
was qualitatively already known: the electric (solid-body) guitar is a very inefficient sound
source – at least as far as the directly radiated primary sound is concerned. However, the
electric guitar is of course not intended to generate primary sound – it is there to generate
electrical voltage. The big difference between the two modes of operation: in the acoustic
guitar, the sound energy needs to travel “through” the body i.e. “through” the wood, while in
the electric guitar the part of the sound energy that is “reflected from the wood to the string”
is captured. Any conjecture that, in the electric guitar, the vibration energy needs to be also
fed to the guitar body as much as possible, is wrong. ”The biggest part of the string vibration
should be conducted into the body. If the latter is fed with unrestrained vibration energy, a
maximum of tone and sustain develops [G&B 12/05]." How should the string ring for a long
time (i.e. have a lot of sustain), if its vibration energy has gone into the guitar body? The law
of energy conservation dictates that energy cannot appear out of nowhere. The excitation
energy is present only once; the part of it that is fed to the guitar body is missing to keep the
string ringing. The banjo is a good example for an instrument that withdraws a lot of energy
from the string within a short time. However the sound of a banjo (and in particular its
sustain!) is not much like that of an electric guitar.7.9 The wood determines the sound?
© M. Zollner & T. Zwicker 2019 Translation into English by Tilmann Zwicker
7-103
From a systems-theory point-of-view, the string represents a mechanical waveguide on
which waves propagate. As these waves impinge on the bridge and the nut (or the fret where
the string is fretted), one part of the energy in the wave is reflected, the other part is absorbed
by the bridge/nut/fret (and adjacent structures). Again, the law of conservation of energy
holds: the sum of the reflected and of the absorbed energy corresponds to the energy in the
wave impinging on the bridge/nut. We get a high rate of absorption if the wave impedance
and the impedance of bridge/nut/fret have comparable values. The wave impedance of the
string (see Chapter 2) depends on the diameter and on the material: typical would be 0.2 Ns/m
(E4-string) to 1 Ns/m (E2-string). These are very small values compared to typical bridge
impedances (100 – 1000 Ns/m). The situation is comparable to an airborne wave that hits onto
a concrete wall: because the wave impedances again differ by several orders of magnitude,
almost all of the sound energy is reflected. The same happens with the string: the vibration of
the string is, for the most part, not fed to the guitar body but it is reflected. In the solid-body
guitar, a degree of reflection of 99.9% for low-frequency partials is not untypical: of the
vibration energy arriving from the direction of the nut, 99.9% are reflected and only 0.1% are
absorbed. There is no other way a vibration could remain for any extended periods of time: if
for the E2-string 50% of the energy would be absorbed at each reflection, only 0.1% of the
initial energy would remain after only 10 reflections – and 10 reflections have happened after
a mere 60 ms for the E2-string! Given a 99.9%-reflection, 37% of the initial energy will
remain after 1000 reflections (that’s 6 s)♣. Therefore, a simple connection exists between the
decay time (the sustain) and the degree of absorption: the higher the degree of absorption, the
shorter the sustain. And here we arrive at an explanation that is not so easy to refute: if the
sound depends on the sustain, and the sustain depends on the absorption, and the absorption
depends on the bridge/nut/fret, then the wood of the guitar body will determine how the guitar
sounds, won’t it, after all?!
Given the intense and controversial discussions about the “tonewood”-topic, let us make a bit
of room for some fundamental considerations: if a string is struck once, its vibration energy
decreases over time. The main reasons for this decay are: sound radiation directly from the
string, internal absorption within the string, and absorption at the string bearings. The first
effect is so small that it is normally neglected. The second effect is significant in the middle to
high frequency range for unwound strings; this is elaborated in Chapter 7.7. The third effect is
the only one that can be connected to body-parameters. If we neglect the first two effects, the
string vibration – and thus a component of the sound – indeed is completely determined by
the guitar body. That is defining the “body” very extensively, though: it would have to
include everything that abuts to the string, in particular the bridge that for example consists of
18 individual components in the case of the Gibson ABR-1 bridge. There is much wailing all
over the place that the super-rare tonewoods of the early Les Pauls are not available anymore,
and thus the sound of these originals will never be duplicated. Interestingly though, the
question rarely asked is to which extent the individual pieces of the ABR-1 bridge were
deburred, and how clean the force fit between the movable bridge saddles and the base is. The
bearing impedances at the bridge and at the nut (or respective fret on the neck) strongly
influence the decay of the individual partials of the sound. Before the vibration energy arrives
in the body, it needs to traverse the bridge/nut/fret; the stronger these elements reflect the
vibration, the less important the material of the guitar body is.
All this is, however, valid for the acoustic guitar, as well – so what is basically different in its
sound generation compared to the electric guitar?
♣ We have neglected other mechanisms of absorption in this exampl"