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Hair tension influence on the vibroacoustic
properties of the double bass bow
Filip Pantelic´
a)
University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, Serbia
filip_pantelic@yahoo.com
Jurij Prezelj
University of Ljubljana, Askerceva 6, Ljubljana, Slovenia
prezelj.jurij@gmail.com
Abstract: The possibility of identifying vibration modes of a double
bass bow, with a non-contact measurement of sound pressure in the
Very Near Field (VNF) was investigated. This paper shows the applica-
tion of this cost-effective method for vibroacoustic testings of the bow.
The spectra of generated tones do not give sufficient information about
a particular bow, but its vibroacoustical behavior provides additional
properties. The visualization for all vibration modes below 4000 Hz was
achieved by using sound pressure scanning in a VNF. Differences in the
vibroacoustical properties of a double bass bow with different hair ten-
sion were analyzed.
V
C2014 Acoustical Society of America
PACS numbers: 43.75.Yy, 43.75.De [DC]
Date Received: June 22, 2014 Date Accepted: September 14, 2014
1. Introduction
The stick-slip effect is essential in the generation of a tone by the bow on any bowed
string instrument. Bow hair, additionally coated with rosin, have properties that cause
it to stick to the string of an instrument. By drawing the bow the string is displaced,
resulting in a transversal force. When the force becomes large enough, the string is
detached and continues to slip along the bow hair. Together, the sticking phase and
the phase of slipping along the hair of a bow, form one cycle that is constantly
repeated when using a bow for playing a continuous tone. The period of this cycle is
the same as the period of the fundamental frequency of a string.
1
In this process, bow
hair vibrate transversally and stretch and compress lengthwise. Hair is attached to the
ends of the bow stick which has its own modes. The influences of bow stick eigenfre-
quencies are reflected to longitudinal bow hair characteristics and thereby to the stick-
slip effect and consequently on the instrument string.
2
While the violin bow is commonly discussed in scientific literature, the bow for
the double bass has not received appropriate attention yet, even though the bow is as
important as the instrument itself, according to musicians. A musician perceives a bow
as an extension of his arm, that enables him to play in various ways. It is more likely
for a musician to find it harder to adjust to a new bow rather than to a new instru-
ment.
3
However, if different double bass bows are used to play the same instrument,
hardly any difference in sound can be noticed, during long and steady notes. Differences
among bows become obvious if the vibrations of a double bass bow are observed.
4
The presented work deals with the following question: Can hair tension influ-
ence the vibroacoustic properties of double bass bow? The starting point of vibration
modes research on the double bass bow is presented in this article, in order to answer
that question and to contribute toward a better understanding of their importance.
a)
Author to whom correspondence should be addressed.
EL288 J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 V
C2014 Acoustical Society of America
F. Pantelic´ and J. Prezelj: JASA Express Letters [http://dx.doi.org/10.1121/1.4896408] Published Online 25 September 2014
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To understand the vibrations of the system, it is usually most common to visu-
alize the vibration response of the system to excitation with a well defined test signal.
Different methods can be applied for vibration modes visualization: Contact measure-
ments using an accelerometer, a laser-scanning vibrometer, Near Field Holography, and
others. NFH is a known method, but not a very often-used one, because of the tradi-
tional belief that measurements of acoustic quantities in the near field lead to a very low
reproducibility and high measurement uncertainty. This is partially true because of a
large number of acoustic minima and maxima that occur above the complex vibrating
structure. The position of a microphone has therefore more influence on the measured
results than the sound source itself. However, by placing the microphone in the Very
Near Field (VNF),
5
just 3 mm above the vibrating structure, measurement reproducibil-
ity increases dramatically.
6
Visualization of vibration modes by scanning the microphone
in the Very Near Field of the vibrating structure was used in the presented experiments.
In such an arrangement, sound pressure above the vibrating structure and under the
microphone is directly proportional to the vibration velocity. The VNF is limited by the
thermal boundary layer of the medium and with the medium viscosity on one side. On
the other side, the VNF is limited by the geometry of the source, on the radiated sound
wavelength and consequently by the sound pressure level decay vs distance ratio.
The Very Near Field above the vibrating surface is defined by the sound pres-
sure level drop of 1 dB, relative to the sound pressure level on the vibrating surface.
6,7
The boundary of the Very Near Field is affected by the size of the antinode a(vibrat-
ing part of the surface between two nodes), and by the shape of the vibrating surface.
In literature, the boundary of the Very Near Field is estimated to 0.11a.
6,7
In such an
arrangement sound pressure above the vibrating structure and under the microphone is
directly proportional to the vibration velocity.
Microphone scanning can be readily used for the visualization of the modal
characteristics of the double bass bow stick by recording the sound emitted from the
vibrating bow stick in the VNF, with some restrictions in the frequency range, back-
ground noise, shape and size of the vibrating structure and acoustic environment.
Bissinger reported in his paper
8
that he used fixed impact hammer excitation in
combination with a moving microphone in VNF for measuring the vibration of bow
hair, and for stick modes he used a fixed accelerometer while hammer excitation was
moved over the bow stick. Measuring hair vibrations this way, it is possible only to regis-
ter transversal vibrations of the bow hair, and not the longitudinal hair vibrations which
are likely to be more important in coupling with bow stick modes.
2
By measuring bow
stick modes while changing hair tension it is possible to distinguish which hair modes,
both longitudinal and transversal, are present due to their coupling with stick modes.
2. Visualization of vibration modes on the double bass bow
2.1. Experiment
In the first experiment, the vibration modes of the double bass bow with a German
frog were scanned with the VNF method. The bow was hung on one side with a thin
flexible string and fixed to the shaker (B&K 4810) at the other side (Fig. 1). Vibrations
on the double bass bow were excited by a shaker, which was driven with an amplifier
using pink noise as a test signal. Such a configuration was used to emulate a vibrating
system with free boundary conditions. Visualizations of vibration modes were per-
formed for two double bass bow conditions: With loosened hair, where the vibration
modes of the double bass bow stick dominate the results, and with tightened hair,
where the double bass bow stick and its hair together compose a composite vibrating
system. The double bass bow presents quite a challenge for the VNF method, because
there is not enough surface area on the round stick to effectively generate sound pres-
sure. Nevertheless, in order to visualize its response, the measuring microphone was
placed in a very near field above the bow stick. A small omnidirectional back electret
microphone (Panasonic WM-61B) was used during the experiments. The distance
F. Pantelic´ and J. Prezelj: JASA Express Letters [http://dx.doi.org/10.1121/1.4896408] Published Online 25 September 2014
J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 F. Pantelic´ and J. Prezelj: Visualization of bow modes EL289
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 93.87.110.178 On: Fri, 26 Sep 2014 05:50:44
between the microphone and the double bass bow stick was kept constant at 3 mm.
The length of the measured bow segment (from the frog to the tip of the bow stick)
was 60 cm. At a distance of 1 cm each, starting from the frog’s end, measurement
points were defined all the way to the tip of the bow. A total of 60 fixed measuring
points were determined along the bow. The sound generated by the vibration of the
bow stick was recorded at each of these points. In order to provide the possibility of
checking the reliability of measurements, the experiment was repeated five times. The
results of the vibration mode visualization by using a sound pressure scanning in a
VNF were achieved for all modes below 4000 Hz.
2.2. Measurement results
The spectra of a sound signal were calculated for each measurement point by using an
FFT size of 4096 points and averaging over 600 samples. Two matrices (60 2048 5)
of signal levels were formed, depending on the position of the bow, the frequency at
which the response was observed, and the repetition of the measurements; one for a
tightened hair and one for a loosened hair on the double bass bow. A graphic repre-
sentation of two matrices, which is shown in Fig. 1, depicts the spatial distribution of
the individual vibration modes of the double bass bow; for loosened hair (Fig. 1, left)
and for the tightened hair (Fig. 1, right). By scanning point by point, the spatial
response of the double bass bow upon excitation is provided, the influence of random
errors is reduced, and the accurate position on the bow can be read on the xaxis. The
gradation of sound level, in the defined positions at the defined frequency, is repre-
sented by white intensity. The lighter parts appear in places where the response of the
bow stick to induced vibrations is of greater intensity, i.e., at the vibration antinodes.
The starting point of the spatial spectrogram represents the position of the frog. The
scanning ends at the tip of the bow, so that the xaxis of the spatial spectrogram repre-
sents the microphone position. The ordered structure of the graph is derived from a
proper spatial distribution of the bow’s vibration nodes and antinodes.
The bow’s own modes are clearly visible in Fig. 1. These eigenfrequencies
appear in the form of horizontal lines composed of brighter spots. An appropriate
reading of the data in the recorded matrices provides a presentation of the spatial
FIG. 1. Visualization of the vibration modes acquired from sound in a VNF on the double bass bow stick for
(a) loose hair, (b) tight hair.
F. Pantelic´ and J. Prezelj: JASA Express Letters [http://dx.doi.org/10.1121/1.4896408] Published Online 25 September 2014
EL290 J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 F. Pantelic´ and J. Prezelj: Visualization of bow modes
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 93.87.110.178 On: Fri, 26 Sep 2014 05:50:44
distribution of double bass bow modes at the desired frequency. In Fig. 2the spatial
distributions of the bow response for two discrete frequencies of 226 Hz (left) and
494 Hz (right) are presented for five repeated measurements. The relative standard
deviation, the ratio between the standard deviation and the mean value, for five
repeated measurements has the average value of 0.09.
3. Influence of hair tension on the vibration modes of the double bass bow
3.1. Experiment
The second experiment was focused on hair tension influence on the vibration modes
of the double bass bow. Hair tension is usually set according to the individual taste of
the musician. However, hair tension is constantly changing while playing. When the
force applied to the bow is increased, for achieving a louder playing sound, the tension
on the bow hair also increases, and consequently changes the vibration modes of the
bow stick. Therefore, it is necessary to understand how the double bass bow stick
behaves at different hair tensions. The experimental setup was the same as in the case
of vibration mode visualization using the VNF method. The response was measured
by a microphone, placed in the very near field at a distance of 3 mm above the bow
stick. The measurement was conducted at a single fixed point that was located in the
upper half of the bow, between 40 and 45 cm from the frog of the bow. The measuring
point was determined in such a way that the measured signal contained the compo-
nents of the three lowest bow modes with the highest response. This kind of setup
enabled observation of the double bass response at these modes by avoiding their
nodes, while tightening and relaxing the hair. Loosening the screws on the bow, in
half-turn steps, the frog position changes causing hair tension changes as well (Fig. 3).
A single step introduces frog movement of about 0.35 mm, and leads to the relaxation
of the hair. In 42 steps, the bow transforms from a fully tight to completely loose state
with the frog moving up to the total of 14.35 mm. After each of these 42 steps of loos-
ening, a 10 s sound sample was recorded by the microphone located at a defined meas-
uring point. Those recorded samples describe the influence of hair tension on bow
vibration modes.
3.2. Measurement results
Changes of the bow’s vibroacoustic properties due to the alterations in hair tension is
depicted in the spectrogram in Fig. 4(left). Values in the spectrogram show how fre-
quency response, measured in the VNF of a vibrating double bass bow, changes due
to the different frog shifting position, i.e., different hair tensions. Two frequency
responses, in the case of extreme stress and for the absolute relaxation of the hair, are
FIG. 2. Tight hair bow vibration modes for five repeated measurements with microphone placed in a VNF of
the bow stick (a) at 226 Hz, (b) at 494Hz.
F. Pantelic´ and J. Prezelj: JASA Express Letters [http://dx.doi.org/10.1121/1.4896408] Published Online 25 September 2014
J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 F. Pantelic´ and J. Prezelj: Visualization of bow modes EL291
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depicted in Fig. 4(right). The spectrum for the strained hair, shown in black, was
raised to 30 dB for better graph visibility. The spectrum of loose hair is shown in gray.
Three characteristic modes are marked with a square, circle, and triangle.
4. Discussion: The effect of hair tension on double bass bow modes
The influence of hair on the double bass bow modes is completely absent if the hair
is loosened. Figure 1(left) therefore represents the vibroacoustic property for the
modes of the bow stick itself. A slightly asymmetrical distribution of nodes and
antinodes originates from variable longitudinal mechanical characteristics of the bow
caused by camber distribution and the taper change along the bow.
3,9
The inhomoge-
neous distribution of mass along the bow stick, as well as the spot where the shaker
is supported, affects the shape of the modes and consequently the appearance of the
graph.
2
ThiscanbeobservedinFig.2. Amplitude is approximately 20% higher at
the end of the double bass bow, where the stick is thinner and with additional mass
at the end.
FIG. 4. (a) Changes of the bow’s vibroacoustic properties due to the alterations in hair tension. (b) Bow’s fre-
quency responses. Gray color for loosened hair, black color for strained hair. The spectrum for the strained hair
was raised to 30 dB for better graph visibility.
FIG. 3. (Color online) Direction of frog shifting caused by loosening the screw.
F. Pantelic´ and J. Prezelj: JASA Express Letters [http://dx.doi.org/10.1121/1.4896408] Published Online 25 September 2014
EL292 J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 F. Pantelic´ and J. Prezelj: Visualization of bow modes
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 93.87.110.178 On: Fri, 26 Sep 2014 05:50:44
The results presented in Fig. 1(left) show, that in case of loosened hair, some
resonances are absent and the response on higher frequencies is generally weaker if
compared with results of the double bass bow with tightened hair (Fig. 1right).
Tightening the hair forms a more complex mechanical system where the resonances of
hair are superimposed over the bow stick characteristic.
Modes on Fig. 4(left) which appear only when the bow is tightened are the
product of coupling between hair and bow stick. Their frequency increases as the hair
tension increases. By tightening the hair only frequencies of some modes were shifted
while frequency of other modes remains unchanged. This can be identified in Fig. 4
(left) by observing the alteration of mode frequencies due to the relaxation of hair.
The frequency of the second mode (226 Hz) is not influenced by hair tightness at all.
This mode is represented as a line parallel with the yaxis. Such modes are the modes
of the bow stick.
The frequency of some bow stick modes changes due to the change of the
physical parameters of the system. Tightening at the ends of the stick creates addi-
tional force which rises as the hair tightness grows. By increasing hair tension, the
camber of a bow lowers, which results in a reduction of bow stick stiffness.
10
The mode marked with a circle (Fig. 4. right) does not change its frequency
when hair is tightened. The frequency of the mode marked by a square rises together
with hair tension, but it also becomes damped. The mode marked by a triangle is
actually a hair resonance
2
that is transferred to the stick and appears only when the
hair is strained.
5. Conclusion
The method for identification of the vibration modes of a bow, by measuring the emit-
ted bow sound in a VNF was used. Emitted bow sound was induced by a shaker,
which was driven with a pink noise test signal. Double bass bow modes are shown for
stretched and loosened hair. The arrangement of modes and the response to noise exci-
tation are the two parameters that reflect the characteristics of a bow. The interaction
of the bow stick and stretched hair was experimentally tested by changing the hair ten-
sion. Visualization of vibration modes revealed two types of modes; modes with fre-
quencies depending on hair tension and modes with frequencies which do not change
with tension. Hair tension also changes while playing. In the case of the double bass,
string vibrating frequencies are low (from 41 Hz), and they are transmitted to the bow
stick through hair-stick coupling. As shown in this paper, the frequency of the first
bow resonance is around 100 Hz, which coincide with the range where the human
vibration sensors threshold has its minimum.
11
A musician can perceive vibrations
with his hand, and this stimulation may affect the musician’s subjective impression of
tone quality. All these features can be used for classifying a bow according to objective
parameters. These measurement methods can be further applied to other string
instruments.
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F. Pantelic´ and J. Prezelj: JASA Express Letters [http://dx.doi.org/10.1121/1.4896408] Published Online 25 September 2014
J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 F. Pantelic´ and J. Prezelj: Visualization of bow modes EL293
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 93.87.110.178 On: Fri, 26 Sep 2014 05:50:44
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EL294 J. Acoust. Soc. Am. 136 (4), Pt. 2, October 2014 F. Pantelic´ and J. Prezelj: Visualization of bow modes
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