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Carnegie Mellon
NSF Grant DMR 0520425
High School Teachers Summer Internship
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2008
Materials Properties of Guitar Soundboards
Paul Longwell
Physics Teacher
Hollidaysburg Area High School
Table of Contents
Activity
1 – Density of Tonewoods
Activity
2 – Young’s Modulus / Strength of Tonewoods.
Activity
3 – Two-Dimensional Resonance Frequency of Tonewoods
Activity
4 – Chladni Patterns of Tonewoods
Activity
5 – Measurement of Soundboard Harmonics Produced on Guitars
Activity
1 – Density of Tonewoods
Activity
2 – Strength of Tonewoods.
Activity
3 – Two-Dimensional Resonance Frequency of Tonewoods
Activity
4 – Chladni Patterns of Tonewoods
Activity
5 – Measurement of Soundboard Harmonics Produced on Guitars
CONTENT
STANDARD A: SCIENCE AS INQUIRY
CONTENT
STANDARD B: PHYSICAL SCIENCE
CONTENT
STANDARD G: SCIENCE AS INQUIRY
Introduction
Tradition=
ally,
soundboards have been made from a variety of natural wood materials, such a=
s spruce,
rosewood, and mahogany. In recent years, however, an increasing number of
synthetic composite materials have emerged as manufacturers attempt to
replicate the acoustic properties of the natural materials while minimizing
undesirable structural problems such as warping, cracking, and general tonal
sensitivity to environmental factors such as temperature and humidity.
To help
students understand the material science applications associated with the
design and engineering of guitars, this project provides students with an
opportunity to quantitatively explore the materials used to manufacture gui=
tar
in such a way that they can construct an understanding of the physical fact=
ors
that affect how a guitar maker’s choice of materials directly affects=
the
performance of the instrument.
To limit =
the
scope of the project, students will focus on the component of the guitar kn=
own
as the soundboard. The soundboard, which is the top surface of the guitar, =
is
commonly crafted out of a material such as mahogany, spruce, maple, or seve=
ral
laminated layers of different types of wood. By conducting experiments on s=
mall
samples of these materials and by making acoustical measurements on guitars
that contain these woods, the students will begin to make meaningful compar=
isons
between these different materials and their usefulness within the context of
this musical instrument.
Where pos=
sible,
including synthetic composite materials would be an excellent addition to t=
his
project. Due to their proprietary nature and cost, these materials can be
difficult to acquire and for this reason were not included in this project.=
Objective
The objec=
tive
of this project is to provide a set of activities to guide students in the
process of characterizing and comparing materials that are currently used to
manufacture the soundboards for acoustic guitars. Through these experiments,
students will become familiar with the field of material science and its da=
ily
applications. Specific goals of the project experiments include:
1. Studen=
ts
will determine the range and intensity of the harmonics that resonate in gu=
itar
soundboards made of different materials.
2. Studen=
ts
will visually observe the various two-dimensional chladni patterns produced=
on
guitar soundboards constructed from different materials.
3. Studen=
ts
will measure physical characteristics of guitar materials that are related =
to
the quality of the sound they produce. The students will conduct experiment=
s to
measure properties such as density and Young’s modulus. The later wil=
l be
calculated using stress vs. strain data from a thin sample of various wood
materials.
To further
compare each type of wood used in making the guitars, thin strips of wood w=
ill
be mounted on vibration drivers to compare the frequency that causes each s=
trip
to resonate.
Background
At
the outset of this project, it must be noted that it is impossible to
completely characterize the performance of an instrument like a guitar sole=
ly
by analyzing a single component such as the soundboard. Although the soundb=
oard
is a crucial component in producing a rich and dynamic tone, there are many
other conditions and materials that work together to produce the range and
depth of sounds produced by the guitar. The materials used in manufacturing=
the
neck, strings, bridge, sides, and back all play important roles and together
create a synergistic effect that cannot completely be analyzed on a
component-by-component basis. While acknowledging this complexity, the
soundboard remains a component of crucial importance whose individual
properties have measurable impact on the overall performance of the guitar.
Therefore, although the limitations of this project are acknowledged, the
soundboard remains a useful focal point for students as they explore the fi=
eld
of materials science through the context of guitars.
![](3D"2008_PaulLongwell_test_files/image006.gif")
![3D"Text](3D"2008_PaulLongwell_test_files/image002.gif")
One
primary reason that the soundboard is such a critical component of the guit=
ar is
that the vibrations created on its surface help to amplify and radiate
vibrations that are first produced on the strings when they are plucked or
strummed. While the materials used in the bridge affect how efficiently the
vibrations are transferred from the strings to the soundboard, the physical
properties of the soundboard itself provide a set of measurable values that
students can calculate and analyze in an effort to make inferences regarding
the acoustic performance of a material. In this project, students are able =
to
use relatively simple methods to determine the density and Young’s
modulus of a specific species of wood. Using these two single pieces of dat=
a,
students can apply rather simple formulas to calculate acoustic values for =
the
wood species such as the speed of sound, impedance, and the sound radiation
coefficient. Furthermore, students can evaluate the usefulness of a specific
wood species in acoustic applications by comparing their data to conglomera=
te
pools of data such as U.G. Wegst’s Natural Materials Selector
shown in the figure below. (Wegst 2006).
![](3D"2008_PaulLongwell_test_files/image010.gif")
![3D"Text](3D"2008_PaulLongwell_test_files/image007.gif")
In
addition to providing students with an opportunity to calculate and compute=
acoustic
measurements, this project also outlines activities for obtaining acoustic =
data
by direct experimentation and observation. To provide a visual representati=
on
of the acoustic vibrations exhibited by various wood species at a given
frequency, researchers have often enlisted the technique of interference
holography. Bernard Richardson was one of the first to utilize this method =
for
his PhD thesis in 1982 at Cardiff University in the UK. The image shown is =
an
example of many displayed by the university at http://www.astro.cf.ac.uk/groups/acoucomp/MAGHolography.html#fotos1.
A rudimen=
tary
version of this technique can be conducted by mounting a guitar top on a wa=
ve driver
and using fine-grained sand to identify nodes and antinodes of vibration on=
the
surface of the wood. A more quantitative analysis of the acoustic performan=
ce
of a guitarsoundboard can be conducted using a soundboard transducer design=
ed
to serve as an electrical pickup for acoustic guitars that lack a built-in
pick-up device. The transducer can be connected to an oscilloscope or other
display device for analysis. In this project, the data is collected by
connecting the transducer to a PASCO voltage sensor and then displaying the
vibration signal as a Fast Fourier Transform (FFT). This type of display al=
lows
students to easily determine the magnitude and duration of harmonic vibrati=
ons
exhibited by the wood surface. A snapshot of this type of data is shown bel=
ow.
The FFT graphs enable students to observe significant discrepancies in the
ability of different materials to sustain vibrations of different frequenci=
es.
This, combined with the density and Young’s modulus data, helps the
students form a basic understanding of the various factors that collectively
determine the suitability of a material for a soundboard. An effective mate=
rial
must possess enough rigidity and strength to support the tension created by=
the
strings, but must also have the structural freedom to resonate across the r=
ange
of frequencies that need to be projected. With a grasp of these issues,
students can begin to evaluate the sound-worthiness of natural and composite
materials based on their physical and acoustic properties.
![](3D"2008_PaulLongwell_test_files/image012.gif")
![3D"Text](3D"2008_PaulLongwell_test_files/image014.gif")
Materials
=
What will=
you
Need?
Activity 1 – Density of Tonewoods
· =
Tonewood Samples (See bibliography for listing of luthie=
rs)
· =
Graduated Cylinder
· =
Balance
Activity 2 – Young’s Modulus / St= rength of Tonewoods
· =
Tonewood Samples (See bibliography for listing of luthie=
rs)
· =
Stress vs. Strain Apparatus (PASCO Scientific)
· =
Computer Interface and DataStudio Software (PASCO
Scientific)
Activity 3 – Two-Dimensional Resonance Frequency of Tonewoods
· =
Tonewood Samples (See bibliography for listing of luthie=
rs)
· =
Wave Generator (PASCO Scientific)
· =
Function Generator or Computer Interface and DataStudio
Software
· =
(PASCO Scientific)
Activity 4 – Chladni Patterns of Tonewo= ods
· =
Guitar tops (See bibliography for listing of luthiers)
· =
Fine-grained sand
· =
Wave Generator (PASCO Scientific)
· =
Function Generator or Computer Interface and DataStudio
Software
· =
(PASCO Scientific)
Activity 5 – Measurement of Soundboard Harmonics Produced on Guitars
· =
Acoustic guitar
· =
Transducer (recommended: Schatten Dualie)
Lesson Plans/ Procedure
Activity 1 – Density of Tonewoods
1.
Select tonewood samples to be used for this activity. Suggested woods inclu=
de
spruce (sitka or englemann), mahogany, cedar, birch, and rosewood.
2.
Cut each type of wood into samples to be distributed to students. Size of e=
ach
sample will depend on the amount available, number of individual samples
needed, and size of graduated cylinder.
3.
Record the mass of each sample on a balance.
4.
Use displacement method in graduated cylinder to determine volume. As an
alternative method, measure dimensions of each sample and calculate the vol=
ume
mathematically.
5.
Calculate the density using the formula D =3D m/V.
Activity 2 – Strength of Tonewoods<= /h2>
1.
Select tonewood samples to be used for this activity. Suggested woods inclu=
de
spruce (sitka or englemann), mahogany, cedar, birch, and rosewood.
2.
Use the template from the stress-strain gauge to cut each type of wood into=
a
sample that can be mounted into the gauge.
3.
Slowly apply stress to the sample using the stress/strain apparatus. Use
DataStudio to record and display the strain exhibited by each sample.
4.
Use the mathematical data from a graph of stress vs. strain to determine
Young’s modulus for each wood sample.
![](3D"2008_PaulLongwell_test_files/image016.gif")
PASCO
Scientific 2008 – Stress vs. Strain Apparatus
Activity 3 – Two-Dimensional Resonance Frequency of Tonewoods
1.
Select tonewood samples to be used for this activity. Suggested woods inclu=
de
spruce (sitka or englemann), mahogany, cedar, birch, and rosewood.
2.
Cut each type of wood into a thin long strip approximately 3/8” wide,
14” long, and 1/8” thick. Best results can be expected with thi=
nner
samples.
3.
Drill a hole in the center of the sample so that the wood strip can be plac=
ed
over the mounting peg on the wave driver.
4.
Secure the wood strip on the wave driver.
5.
Using DataStudio, vary the oscillation frequency of the wave driver and obs=
erve
the amplitude of vibrations experienced by the end of the wood strip. Note =
the
frequencies that produce relatively large vibrations when compared to those
produced by other frequencies.
6.
Record the frequencies that cause the wood strip to exhibit resonance for e=
ach
type of wood. From the recorded frequencies, determine the fundamental
frequency for each strip. Compare the magnitude of the fundamental frequenc=
ies
for different tonewoods.
![](3D"2008_PaulLongwell_test_files/image018.gif")
PASCO
Scientific 2008 - Resonance Strip Apparatus
Activity 4 – Chladni Patterns of Tonewo= ods
1.
Drill a hole at the center of mass of each guitar top so that the top can be
placed over the mounting peg on the wave driver.
2.
Secure the guitar top on the wave driver.
3.
Sprinkle a moderate amount of fine-grained sand on the guitar top.
4.
Using DataStudio, slowly vary the oscillation frequency of the wave driver =
and
observe nodes and antinodes in the surface of the guitar top.
Use
a digital camera to record and compare the unique patterns exhibited by each
type of wood used for the guitar tops.
![](3D"2008_PaulLongwell_test_files/image020.gif")
PASCO
Scientific 2008 – Violin Chladni apparatus, similar to setup for guit=
ar
soundboard
Activity 5 – Measurement of Soundboard Harmonics Produced on Guitars
1.
Use acoustic putty (usually included with the transducer) to mount the
transducer to surface of the guitar’s soundboard. For each guitar,pla=
ce
the transducer at the same location. For example, you may wish to center the
transducer approximately 3/4” behind the bridge.
2.
Use alligator clips to connect the plug of the transducer to a voltage sens=
or.
3.
Create a FFT display (Fast Fourier Transform) using Datastudio and set the
sample rate to approximately 2500 samples per second.
4.
Pluck each string individually and observe the harmonics exhibited by the
soundboard.
5. Use a screen video capture program (ala www.jing.com) to
create a time record of the harmonics. Play the recording back and determine
the duration of the vibrations for each harmonic.
6. Compare the ability of each wood to sustain vibrations of
different frequency ranges.
![](3D"2008_PaulLongwell_test_files/image022.gif")
Lab Results
Data:
The graphs below show the ability of three common soundboard
materials to
sustain vibratio=
ns
produced by each of the six guitar strings.
![](3D"2008_PaulLongwell_test_files/image024.gif")
![](3D"2008_PaulLongwell_test_files/image026.gif")
![](3D"2008_PaulLongwell_test_files/image028.gif")
![](3D"2008_PaulLongwell_test_files/image031.gif")
![](3D"2008_PaulLongwell_test_files/image048.gif")
![](3D"2008_PaulLongwell_test_files/image049.gif")
Learning Outcomes
Education=
al
Standards used and/or met
CONTENT STANDARD A: SCIENCE AS INQUIRY
A1. Abilities necessa=
ry to
do scientific inquiry:
Identify questions and
concepts that guide scientific investigations.
Design and conduct a
scientific investigation.
Use technology and
mathematics to improve investigations and communications.
Formulate and revise =
scientific
explanations and models using logic and evidence.
Recognize and analyze
alternative explanations and models.
Communicate and defen=
d a
scientific argument.
A2. Understanding abo=
ut
scientific inquiry:
Scientists usually in=
quire
about how physical, living, or designed systems function.
Scientists conduct
investigations for a wide variety of reasons.
Scientists rely on
technology to enhance the gathering and manipulation of data.
Mathematics is essent=
ial in
scientific inquiry.
Scientific explanatio=
ns must
adhere to criteria such as a proposed explanation must be logically consist=
ent;
it must abide by the rules of evidence; it must be open to questions and
possible modification; and it must be based on historical and current
scientific knowledge.
Results of scientific
inquiry emerge from different types of investigations and public communicat=
ion
among scientists.
CONTENT STANDARD B: PHYSICAL SCIENCE
B2. Structure and
properties of matter
B4. Motions and force=
s
B6. Interactions of e=
nergy
and matter
CONTENT STANDARD G: SCIENCE AS INQUIRY
G1. Science as a human
endeavor: Individuals and teams have contributed and will continue to
contribute to the scientific enterprise.
Scientists have ethic=
al
traditions. Scientists are influenced by societal, cultural, and personal
beliefs and ways of viewing the world.
G2. Nature of scienti=
fic
knowledge: Science distinguishes itself from other ways of knowing and from
other bodies of knowledge.
Scientific explanatio=
ns
must meet certain criteria. Because all scientific ideas depend on experime=
ntal
and observational confirmation, all scientific knowledge is, in principle,
subject to change as new evidence becomes available.
Other Data/Info
Bibliography of Resources
Gough,
Colin. Science and the Stradivarius. Physics World. April 1,
2000.
Archived
online at http://physicsworld.com/cws/article/print/696
Ratner,
Brad. Guitars, Wood, and Tone. Harmony Central. April 26.
1999.
Archived
online at http://www.harmonycentral.com/Guitar/Articles/Guitars_Wood_A=
nd_Tone/
Richardson,
Bernard. Accessed July 23, 2008.
http://www.astro.cf.ac.uk/groups/acoucomp/MAGHolography.html#fotos1
Wegst,
Ulrike G. K. Wood for Sound. American Journal of Botany.
2006;
93:1439-1448
Suggested Luthiers
Allen
Guitars & Luthier Supplies
PO Box
1883
Colfax,
CA 95713 USA
1-800-953-3035
Comins
Guitars
PO
Box 611
Willow
Grove, PA 19090
(215)
376-0595
Luthiers
Mercantile International, Inc.
7975
Cameron Dr.
Bldg.
1600
Windsor,
CA 95492
Tel:
707-687-2020
1-800-477-4437