A field study of the exposure-annoyance relationship of military shooting noise.

TL;DR: The sound exposure level L(E) of shooting noise better explained variations in annoyance than other operational and/or acoustical predictors.

Abstract: This article reports a field study on noise annoyance from military shooting with small, midsize, and heavy weapons that was carried out among 1002 residents living near eight different training grounds of the Swiss army. The goal of the study was to derive the exposure-annoyance relationship for military shooting noise in communities in the vicinity of average military training grounds. Annoyance was determined in a telephone survey by means of the 5-point verbal and 11-point numerical annoyance scale recommended by the International Commission on Biological Effects of Noise. Exposure was calculated using acoustical source models of weapons and numbers of shots fired, as recorded by the army. Annoyance predictor variables investigated were LAE, LCE, LCE−LAE, number of shots above threshold, as well as individual moderators. Exposure-annoyance relationships were modeled by means of linear and logistic regression analyses. The sound exposure level LE of shooting noise better explained variations in annoyan...

Summary

Introduction

• Here the authors present a similar study to analyze the combined rotational and translation states of hydrogen molecules confined in a one-dimensional potential.
• In the present paper, the authors focus their attention on the general formalism and discuss only the case where a single H2 is confined inside a single nanotube.
• In Sec. VI the authors discuss the experimental observation of various transitions via inelastic neutron scattering measurements.
• The authors conclusions are summarized in Sec. VII.

II. POTENTIAL MODEL

• By this the authors mean that the potential produced by the nanotube has cylindrical symmetry and is invariant with respect to translations along its axis of symmetry.
• It is instructive to look at various potentials for an orientationally averaged hydrogen molecule ~i.e., parahydrogen with J50) when H2 is inside and outside a single nanotube.
• The solid and dashed lines in Fig. 2 show the results with and without the smooth tube approximation, respectively.

III. FORMULATION

• The hydrogen molecule is unique in that its moment of inertia is small enough that the rotational kinetic energy often dominates the orientational potential in which the molecule is placed.
• This function may be evaluated by integrating the potential at a fixed center-of-mass position over all orientations vL M~r !5eiMfrE dVY LM~u ,f!*V~r,V!. ~6!.
• It is important to keep in mind that vL M(r) vanishes for odd M.
• As a consequence, in the (2J11)-component wave function there is no mixing between even and odd values of M.

1. Harmonic potential

• Here the authors discuss the eigenvalues and eigenfunctions of the two-dimensional isotropic harmonic oscillator, to emphasize the relation between the above formulation in terms of cylindrical coordinates and that in terms of Cartesian coordinates.
• This degeneracy reflects the U2 symmetry corresponding to the invariance of the Hamiltonian with respect to a transformation of the form S ~ax†!8~ay†!8D 5@U#S ~ax†!~ay†!D , ~14!.
• This transformation is essentially the same as a four-dimensional rotational symmetry in the space of the momenta px , py , and coordinates x and y.
• Here the family of solutions for a given value of m are labeled a50,1,2, . . . , in order of increasing energy and for the isotropic and harmonic potential the authors have Em a5~m1112a!\v .
• A consequence of this symmetry is that for a harmonic potential the total energy depends only on the total number of phonon excitations.

2. Anharmonic potential

• The U2 symmetry is broken by anharmonic terms which then take us into the generic case of a particle in a circularly symmetric potential which is not harmonic.
• Accordingly, the authors now consider the effect of adding an anharmonic perturbation of the form gr4 to the harmonic potential.
• The authors results are characteristic of the generic case, for which different values of m give rise to distinct eigenvalues.
• The n-fold degenerate manifold which has energy n\v for the harmonic potential is split into doublets ~corresponding to the degeneracy between 1m and 2m) and, if n is odd, a singlet from m50.
• The authors explicit results are given in Table I.

B. Toy model of translation-rotation coupling

• In this section the authors explore the consequences of allowing coupling between rotations and translations.
• For larger tubes, the minimal potential energy occurs for a nonzero value of r and the molecule is dominantly off center.

C. Results of the toy model

• The authors now discuss the results of the toy model assuming that the number of phonons is a good quantum number.
• The authors note that all the energy expressions given below are with respect to BJ(J11) with J51.

1. Zero phonon manifold

• The authors first consider the manifold of the states having J51 with zero phonons.
• One has the singlet Jz50 state lower than the doublet Jz561 states by an energy separation of 3a .
• One may visualize this as the energy difference between a state for which the molecule is in the phonon ground state and is oriented parallel to the axis and the two states when the molecule is in the phonon ground state and is oriented transversely to the axis.
• For later use the authors tabulate these wave functions in Table II.

2. One-phonon manifold without rotation-translation coupling

• If the authors set b50 in the toy model of Eq. ~19!, then essentially they have independent oscillation of molecules which have fixed orientation.
• So that the lowest energy state ~if a.0) is doubly degenerate and the excited state is fourfold degenerate, as is shown in Fig.

3. One-phonon manifold with rotation-translation coupling

• The unphysical aspect of the energy level scheme the authors just found for the one-phonon manifold is that it does not take into account that the molecular orientation ought to be correlated with the translational motion.
• This means that the orientation of the molecule has to be correlated with the translational motion.
• In terms of number operators nx and ny which are the number of phonon excitations in the x and y directions, respectively, and ax † and ay † which are creation operators for aWe tabulate the energy relative to \v .the authors.
• This argument predicts that the six states form three doubly degenerate energy lev- els.
• In Fig. 4 the authors show the energy levels when no dynamical mixing between rotations and translations is allowed, i.e., for b50.

4. Two-Phonon manifold with rotation-translation coupling

• Actually, because the dependence on r of the matrix elements in Eq. ~19! was taken to be either constant or proportional to r2, the representation of Eq. ~22!.
• The removal of the degeneracy in the energy level scheme of the two-phonon ~i.e., nx1ny52) and (J51) manifold according to the Hamiltonian of Eq. ~22!.
• Is shown in Fig. using the WS77 potential are given in the last column of Table V.18.
• In this simple model the authors also include the anharmonic term gr4 which they treat within first order perturbation theory.
• The authors determine the best parameters for the toy model by making a least squares fit of the numerically determined energy levels to those of the toy model and these parameters as well as the results of this fit are given in Table.

5. Summary

• The authors can summarize the systematics of the rotationtranslation spectrum of the toy model they have introduced.
• The authors first consider the harmonic g50 case and then discuss the effect of introducing anharmonicity.
• Harmonic phonon states which transform as (x 1iy)N22k will uniquely combine with Jz50 states to form states for which P5(N22k) and which have energy (N 11)\v22a .
• Since the rotation translation coupling interaction proportional to xy(J1 2 2J2 2 ) has matrix elements between these two states, the eigenstates f16f2 will be split by an amount proportional to bs2 and this splitting will be modified by anharmonicity.

V. MEXICAN HAT POTENTIAL

• Here the authors discuss the case when the minimum of the potential V0(r) occurs for nonzero r as happens for H2 molecules inside 10310 tubes or for H2 molecule in a bound state outside any tube.
• It is possible to understand the quadratic behavior of energy levels versus the quantum number P based on a simple idealized model.
• The authors expect the radial wave functions to be Gaussians centered about r5r0.

OF THE ENERGY SPECTRUM

• Here the authors make some remarks concerning the observation of these modes via inelastic neutron scattering.
• Also the cJ ,P (a) (k ,m)’s are the set of coefficients ~for fixed J, P, and a) which are obtained by the numerical solution of the (2J11)-component radial eigenvalue problem on a set of mesh points $rk%.

A. Para to ortho conversion

• At low temperature the initial state ~whose energy is denoted Ei) will be the ground state for J50 and for a small value of P ~which the authors denote Pi).
• The authors now discuss the qualitative meaning of this result.

B. Ortho Cross Section

• Here the authors discuss the scattering from an ortho H2 molecule.
• The resolution at energies below around 10 meV could be about 0.5 meV ~which is used in Fig. 8! and therefore it may be possible to observe these transitions.
• Finally the authors note that the tangential phonon transitions below 10 meV show a maximum near 3.6 to 4 meV.
• The phase change when the neutron passes through a diamater of the Maxican hat is 2kr0, where r0 is the radius at which the Maxican hat potential is minimal.

VII. CONCLUSION

• The authors list the major conclusion from their study of H2 molecules bound to nanotubes which they treat as smooth cylinders.
• This formulation leads to classifying translation-rotation wave functions according to their properties under a global rotation of the molecule about the cylindrical axis.
• The quantum wave functions are easy to understand qualitatively.
• This simplification is a result of the mirror plane perpendicular to axis of the cylinder.
• The authors also suggest that neutron time-of-flight spectra could provide useful confirmation of their results.

Figures

FIG. 1. Logistic dose-response curves and 95% confidence intervals for three different methods of defining the percentage of highly annoyed persons in the current sample. The curve based on the 5-point verbal scale that uses a cutoff point of 72% was generated by weighting the cases, where the respondent chose the “very” modifier on the scale, with 0.4 in the logistic regression analysis.

TABLE IV. Logistic regression analysis results of PHA explained by LAE and individual moderators. Noise sensitivity was assessed using the LEFK questionnaire and is expressed on a scale from 0 to 27. Attitude toward the army is expressed on a scale from 1 to 5.

TABLE V. Results of the logistic regression analyses of PHA with LAE or LCE as only predictor.

TABLE III. Mean annoyance and percent highly annoyed %HA for different degrees of exposure. The categories are defined based on the LAE metric, the average exposure values -LAE and -LCE pertain to the arithmetic average of all cases within the category boundaries. N refers to the number of cases in each exposure level category.

Full text

A field study of the exposure-annoyance relationship of military
shooting noise
Mark Brink
a兲
D-MTEC Public and Organizational Health, ETH Zurich, CH-8092 Zurich, Switzerland
Jean-Marc Wunderli
Laboratory of Acoustics, Empa Swiss Federal Laboratories for Materials Testing and Research, CH-8600
Duebendorf, Switzerland
共Received 20 April 2009; revised 15 December 2009; accepted 6 February 2010兲
This article reports a field study on noise annoyance from military shooting with small, midsize, and
heavy weapons that was carried out among 1002 residents living near eight different training
grounds of the Swiss army. The goal of the study was to derive the exposure-annoyance relationship
for military shooting noise in communities in the vicinity of average military training grounds.
Annoyance was determined in a telephone survey by means of the 5-point verbal and 11-point
numerical annoyance scale recommended by the International Commission on Biological Effects of
Noise. Exposure was calculated using acoustical source models of weapons and numbers of shots
fired, as recorded by the army. Annoyance predictor variables investigated were L
AE
, L
CE
, L
CE
−L
AE
, number of shots above threshold, as well as individual moderators. Exposure-annoyance
relationships were modeled by means of linear and logistic regression analyses. The sound exposure
level L
E
of shooting noise better explained variations in annoyance than other operational and/or
acoustical predictors. Annoyance on the 5-point scale was more closely related to noise exposure
than expressed on the 11-point scale. The inclusion of the C-A frequency weighting difference as a
second explaining variable, as suggested earlier, did not substantially enhance the predictability of
high annoyance. © 2010 Acoustical Society of America. 关DOI: 10.1121/1.3337234兴
PACS number共s兲: 43.50.Qp, 43.50.Pn, 43.50.Sr 关BSF兴 Pages: 2301–2311
I. INTRODUCTION
A. Study rationale
Exposure-response relationships are commonly used to
assess the annoyance impact of many kinds of traffic or in-
dustrial noise. In their most common form, they relate noise
exposure to the percentage of highly annoyed persons
共%HA兲. As military shooting noise 共as a result of military
training activities in times of peace兲 is less of a problem for
the majority of the population, there exist only a few field
studies in the literature that investigated its effects. Hence the
impact of military shooting noise from training grounds of
armies is far less well understood than effects of other noise
sources. The goals of the current study were thus the estab-
lishment of a statistical model that explains variation of com-
munity annoyance by operational and acoustical descriptors
of military shooting activity and to provide an exposure-
effect function for high annoyance 共%HA兲 among residents
in the vicinity of typical military training grounds in Swit-
zerland.
Despite a relatively large body of literature, which
mostly pertains to laboratory studies 共
Meloni and Rosen-
heck, 1995
; Schomer et al., 1994; Vos, 2001, 2003; Vos and
Geurtsen, 2003
兲, there have only few exposure-effect func-
tions for 共military兲 shooting noise been published so far 共e.g.,
in
Schomer, 1985兲. In the real-world situation, people use
adaptive mechanisms that try to ignore noise as much as
possible, whereas in a laboratory setting they do the opposite
and inevitably concentrate on the noise. This provides a
strong rationale to investigate shooting noise effects in the
field, at the homes of the affected population.
The current study was carried out in Switzerland, where
one can find several multipurpose training grounds where
military shooting activity comprises small, middle, and
heavy weapon shooting in one and the same place, and, be-
cause plain space is very scant, often in close vicinity to
inhabited areas. This specific geographic situation therefore
appears to be well suited to investigate military shooting
noise annoyance by means of a field study. At this point, the
notion is relevant that this study is not primarily about the
effects of large army weapons such as tanks or artillery, since
the number of rounds of such types of weapons each year is
considerably lower than from small caliber arms.
B. Shooting noise descriptors and exposure-effect
relationships
While exposure assessment following the equal energy
principle has been adopted for the most distinctive noise
sources, at least pertaining to annoyance as dependent vari-
able, no commonly accepted noise descriptor for assessing
community annoyance to shooting noise has successfully es-
tablished itself to date. Of the few field studies on commu-
nity annoyance due to weapon noise at hand 共
Buchta and
Vos, 1998
; Bullen and Hede, 1982; Fidell et al., 1983; Lev-
ein and Ahrlin, 1988; Rylander and Lundquist, 1996;
a兲
Author to whom correspondence should be addressed. Electronic mail:
brink@ethz.ch
J. Acoust. Soc. Am. 127 共4兲, April 2010 © 2010 Acoustical Society of America 23010001-4966/2010/127共4兲/2301/11/$25.00
EMPA20100095

Schomer, 1985; Schomer et al., 1994; Sorensen and Magnus-
son, 1979
兲, only few exposure-effect functions explaining
annoyance due to a mixture of different kinds of army weap-
ons emerged.
In the literature, noise descriptors that were identified to
yield the highest degrees of explained variance of annoyance
from impulsive sounds vary from accumulated peak level
共
Bullen et al., 1991兲, maximum sound pressure level 共Levein
and Ahrlin, 1988
兲, A-weighted FAST maximum sound pres-
sure level 共
Sorensen and Magnusson, 1979兲, number of shots
above a C-weighted threshold level 共
Rylander and Lun-
dquist, 1996
兲, C-weighted average day-night level L
CDN
共
Schomer, 1985兲, and Schomer’s 共Schomer, 1994兲 “new de-
scriptor for high-energy impulsive sounds” 共
Buchta and Vos,
1998
兲, the L
Aeq
, to even surrogate measurements of ground
vibration in the case of blast noise from surface mines 共
Fidell
et al., 1983
兲. Most of these studies investigated the noise
effect from particular source 共weapon兲 types, either from,
e.g., rifle shooting ranges or from large weapon training fa-
cilities. Shooting with firearms on multipurpose training
grounds with different combinations of small to very large
caliber weapons creates a complex blend of different sounds.
It therefore appears that the construction of an all-purpose
exposure-effect curve regarding military shooting noise is
much more difficult than for other more uniform noise types.
Depending on the predominant weapon type used, one or the
other noise descriptor probably better predicts community
annoyance. For example, noise annoyance from large weap-
ons which also elicit rattle and vibrations might better be
predicted using a C-weighted measure than an A-weighted
measure. The question which predictor best accounts for the
variation of military shooting noise annoyance in general,
that means for any kind and combination of weapons, cannot
easily be answered.
C. Frequency weighting
The question of the choice of frequency weighting to
best predict impulsive or weapon noise annoyance respec-
tively has received considerable attention in the literature.
Insights into the relationship between shots of weapons and
annoyance, especially with regard to impulse correction and
frequency weighting have been collected in a series of labo-
ratory studies 共
Meloni and Rosenheck, 1995; Schomer and
Wagner, 1995
; Schomer et al., 1994; Vos, 1990, 2001兲. The
use of the A-weighting is widespread in the evaluation of
gunfire noise from small arms, usually including a penalty
correction of between 5 and 12 dB for the added annoyance
of impulsive sounds 共
Buchta, 1990; Vos, 1990兲. However,
for the assessment of large caliber or high-energy weapon
noise, the C weighting and the measure L
CE
共or L
CDN
兲 have
been suggested in the past 共
Schomer, 1986兲 or are recom-
mended in ISO 1996-1 共
International Standards Organisa-
tion, 2003
兲. The assessment methodology applied in many
European countries uses L
AF,max
共Germany, Switzerland兲 or
L
AI,max
共Austria, Finland, Denmark, Norway, and Sweden兲
for small arms, and C-weighted measures such as L
CE
共Fin-
land, Norway, Sweden兲 and L
Ceq
共Germany, The Nether-
lands, and Denmark兲 for large weapons.
For the whole set of impulse sound types produced by
various firearms ranging in caliber from 7.62 to 155 mm, the
annoyance rating in the laboratory study of
Vo s 共2001兲 was
almost entirely determined by the “outdoor” L
AE
of the im-
pulses, as long as the artificial laboratory situation reflected a
scenario with open windows. Similar results were reported
by
Meloni and Rosenheck 共1995兲 who found that if shooting
noise is predominantly heard through open windows, the
A-weighted sound exposure level is appropriate for predict-
ing annoyance.
Vo s 共2001兲 suggested to include the difference between
the C- and A-weighted levels as a second annoyance predic-
tor alongside the A-weighted level as principal predictor
共
Vos, 2001兲. Because the addition of the C-weighted level in
the regression equations in most instances only very slightly
increased the explained variance of the exposure-effect rela-
tionship, it remains arguable, whether the additional effort of
C-weighted measurements and/or calculations is justified,
particularly for the assessment of the “outside situation,” as
Vo s 共2001, 2003兲 demonstrated in his laboratory studies. It is
therefore desirable to empirically test the advantage of the
incorporation of C-weighted measurements not only in the
laboratory but also within the scope of community reaction
surveys in the field, such as the present one.
II. METHODS
A. Sampling procedure
Depending on the site-specific combinations of
weapons/ammunition used, average distances of dwellings
from the shooting ground, the degree of visibility of army
activities in the surrounding neighborhood, involvement with
the army 共e.g., as employee兲, and many other factors, one
would expect exposure-effect relationships for annoyance to
show a rather wide variation. As the primary goal of the
study was collecting data for constructing an exposure-effect
relationship, a representative amount of residents near the
eight largest training grounds of the Swiss army, that were
located sufficiently close to inhabited areas to potentially
evoke annoyance reactions from noise, were sampled. The
corresponding sites were the army training grounds of Bière,
Thun, Wangen an der Aaare, Gehren-Erlinsbach, Krähtal-
Riniken, Walenstadt, Herisau-Gossau, and Chur. At each of
these eight sites, the exposure contours from preliminary ex-
posure calculations 共that did not account for elevation above
ground and shielding effects from neighboring buildings兲
were used to assign exposure values to building addresses
using a GIS system provided by the Swiss statistics office.
The exposure was calculated as the yearly sound exposure
level L
AE
, i.e., the total acoustic energy resulting from shoot-
ing activity during an entire year. At each of the eight sites,
the primary sampling area was defined as the area that was
enclosed by the 104 dB L
AE
exposure contour. Each address
was then assigned an exposure stratum 共104–107, 107–110,
110–113, 113–116, 116–119, 119–122, 122–125, 125–128,
and ⬎128 dB兲. Over all eight sites, a total of 5901 building
addresses within the 104 dB共A兲 contour were identified.
These addresses were aligned with a commercial address da-
tabase to yield all available landline telephone numbers of
2302 J. Acoust. Soc. Am., Vol. 127, No. 4, April 2010 M. Brink and J. M. Wunderli: Annoyance from military shooting noise

households. 5851 individual telephone numbers were identi-
fied. The telephone numbers were stored together with their
exposure level category and served as the primary sample.
The survey was carried out by computer assisted telephone
interviews 共CATIs兲. Within each household, one person over
16 years of age was selected using a modified Troldahl–
Carter method 共
Troldahl and Carter, 1964兲. The CATI soft-
ware was configured to try to sample equal amounts of sub-
jects in the different exposure strata, as far as possible. 5851
individual numbers were called. A total of 1002 interviews
could be realized. 2137 calls were either never answered or
were not valid due to technical reasons 共e.g., a FAX device at
the other end of the line兲. Of the 3714 remaining calls that
resulted in a voice contact, the following statistics apply:
Valid interviews conducted: 27%; interview scheduled, but
did not take place for unknown reasons: 8%; communication
or language problems make interview impossible: 4%; no
target person living in household: 2%; person called refused
interview: 59%.
B. Telephone interviews
Interviews lasted about 15–20 min and took place during
the evening hours of September, October, and November
2007. The schedule moved gradually from questions about
the satisfaction with the immediate environment to the topic
of military shooting noise. The true aim of the survey was
disclosed to all interviewees only after the interview was
finished and they were given the opportunity to withdraw, an
option no one exercised.
For the interviews, a questionnaire was used that first
asked about various criteria of living quality of the inter-
viewee, among them, noise exposure and annoyance from
different sources 共five-point verbal scale, including military
shooting noise兲. These were asked in random order of the
sources, followed by the items of the short form of the
“Lärmempfindlichkeitsfragebogen” 共LEFK; English: “Noise
sensitivity questionnaire”兲 by
Zimmer and Ellermeier 共1998兲
to assess noise sensitivity. In the middle of the interview, the
main block about military shooting noise exposure and an-
noyance was placed. This main block of questions included
the German version of the 11-point annoyance scale from 0
to 10 recommended by the International Commission on
Biological Effects of Noise 共ICBEN兲 that were published by
Fields et al. 共2001兲, a question about strategies to cope with
the noise, and three items about the respondent’s attitude
toward the army 共these items were “Switzerland does need
an army,” “The Swiss army sufficiently cares for the envi-
ronment,” and “Military shooting noise is a necessary evil”兲
that had do be answered ona1to5scale with the end points
“totally agree” and “totally disagree.”
C. Exposure assessment
After the selection of the eight study sites and the col-
lection of the survey data, the relevant source data for the
final 共high detail兲 noise exposure calculations were collected
from army officials that were in command of the respective
training grounds. Their task basically encompassed the re-
porting of the weapons and ammunitions used, the corre-
sponding number of shots and shooting days, as well as the
distribution of shots fired between day and evening 共night
shootings were very rare兲. Each weapon/ammunition combi-
nation was assigned one of the following categories: small
caliber 共⬍10 mm, e.g., assault rifles兲, middle caliber 共10–
100 mm, e.g., antiaircraft guns兲, large caliber 共⬎ = 100 mm,
e.g., large tank cannons兲, grenades and explosive charges,
mortars, and practice ammunition.
For all receiver points in the survey, the exposure from
every emplacement/weapon/ammunition combination of the
respective study site was calculated using the “WL04”
source and propagation model developed by the Swiss Fed-
eral Laboratories for Materials Testing and Research 共Empa兲.
This model delivers exposure spectra in octave bands from
31.5 Hz to 4 kHz of direct and reflected sounds as well as for
each source and receiver combination and for up to 16 dis-
tinct weather conditions that were derived for each study site
based on long-term weather statistics 共the 16 Hz octave band
was omitted as it does not relevantly contribute to the total
exposure, even for large weapons兲. The model accounts for
three types of sound sources: muzzle blasts, sonic booms,
and detonations. Receiver points were set on the facade of
the building aiming at the shooting ground. The height of the
receiver points was set to 1.8 m for detached houses and
ground floor apartments. For each additional floor, the height
was increased by 2.6 m. Exposure calculations were per-
formed separately for the years 2004, 2005, and 2006 and
separately for daytime and evening shootings. Shootings in
the night past 23:00 h were extremely rare, as were shootings
during weekends.
The total yearly exposure levels were calculated as the
sum of the energetic products of each emplacement/weapon/
ammunition sound exposure level with their corresponding
number of shots fired in the respective year.
As the timely distribution of the intensity of shooting
often varies considerably across a year, a 共daily兲 average
exposure value, e.g., a 12 h L
eq
ora24hL
eq
, does not in
most cases reflect a meaningful description of the noise ex-
posure residents are affected with. Dose values in this article
are therefore simply given as L
E
values, representing the to-
tal 共integrated兲 energy of shooting noise exposure in a year
共or as the average over 3 years兲. A corresponding energy
equivalent continuous level over a particular time period can
be obtained by transforming the given L
E
value, e.g., using
L
eq
= L
E
− 10 log共N
SD
⫻ N
HD
⫻ 3600兲,
共1兲
where L
eq
is equivalent sound level for a particular number
of hours of a particular number of days 共within a year兲, N
SD
is number of days in a year when shootings/trainings take
place, N
HD
is number of hours per day for which the average
sound level should be calculated 共e.g., 12兲. For example, the
average daily 12 h L
eq
would thus be L
E
−10 log共365⫻12
⫻3600兲.
III. RESULTS
A. Sample description
A total of 460 male 共46%兲 and 542 female 共54%兲 par-
ticipants constituted the sample of 1002 residents. Shooting
J. Acoust. Soc. Am., Vol. 127, No. 4, April 2010 M. Brink and J. M. Wunderli: Annoyance from military shooting noise 2303

noise exposure was calculated for 918 distinct receiver
points. For a small number of the receiver points, more than
one respondent were interviewed 共e.g., more than one family
member living in the same apartment兲. 232 interviews were
made in the French speaking part of Switzerland. Respon-
dents were in the age range from 16 to 94 years. The average
age of the respondents was 50 years. The age class distribu-
tion was as follows 共in parentheses are the percentages of the
population older than 16兲: between 16 and 20 years: 5%
共5%兲; 20–40: 25% 共34%兲; 40–60: 37% 共34%兲; and older
than 60 years: 33% 共26%兲.
The respondents experienced yearly military shooting
noise exposure levels at their homes between 92 and 130 dB
L
AE
or 98 and 141 dB L
CE
, respectively. Unlike the 共quite
simple兲 preliminary calculations that were used for sample
stratification and definition of the address sampling areas, the
definitive exposure calculation for each respondent ac-
counted for the elevation above ground and shielding effects
from other buildings; thus yearly L
AE
levels down to 92 dB
were reached in the sample. Table
I shows the distribution of
the number of telephone interviews that were realized per
L
AE
exposure level category 共as 3 year energetic average兲
and study site.
Table
II shows the yearly average number of shots as
well as the number of shots above the 50, 60, 70, and 80 dB
L
AE
thresholds per weapon type, as experienced at the 918
receiver points in the sample. The figures given in the last
four columns represent the average number of shots above
the respective threshold, which is defined as the average
A-weighted sound exposure level of one individual shot of a
distinct source 共more clearly the emplacement/weapon/
ammunition combination兲 at the receiver points within the
study sample, as the average of the 3 years 2004, 2005, and
2006.
The average shooting activity per year was about the
same for all 3 years and no substantial changes have oc-
curred at any of the eight grounds between 2004 and 2006.
B. Annoyance ratings and exposure metrics
In light of the different approaches to define high annoy-
ance and for reasons of comparability, both ICBEN scales to
assess 共high兲 annoyance in the respondent 共
Fields et al.,
2001
兲 were part of the interview. Concerning the five-point
verbal scale, ICBEN’s recommendation is to use the upper
two categories 共the verbal marks “very” and “extremely”兲 as
indicators of high annoyance. This corresponds to a cutoff
point at 60% of the scale. No recommendation is given for
the 11-point scale, but according to common practice, the
upper three points on the numerical scale 共8, 9, 10兲 define the
presence of “high annoyance” in the respondent. In this case,
the cutoff lies at 72.7% 共see Schultz, 1978兲. In total, on the
11-point numerical scale, 170 of 1002 respondents qualified
as highly annoyed, on the 5-point scale 241 of 1002.
The annoyance questions were asked in the following
order: the first time during the interview using the 5-point
verbal scale with the marks “not at all,” “slightly,” “moder-
ately,” “very,” and “extremely” within a block of noise an-
noyance questions for different noise sources, and the second
time later during the interview using the 11-point numerical
scale. For all further quantitative analyses, the verbal answer
alternatives of the five-point scale have been transformed to
numerical values 1–5 and treated as continuous.
TABLE I. Number of interviews conducted at each study site and per exposure category.
Study
site
90–95 dB
关L
AE
兴
95–100 dB
关L
AE
兴
100–105 dB
关L
AE
兴
105–110 dB
关L
AE
兴
110–115 dB
关L
AE
兴
115–120 dB
关L
AE
兴
120–125 dB
关L
AE
兴
125–130 dB
关L
AE
兴
Bière 14 21 50 42 51 42 10
Chur 1 15 62 56 23 2
Gehren-Erlinsbach 2 6 11 8 2
Herisau-Gossau 11 25 20 7 1 2
Krähtal-Riniken 1 5 25 16 10 1
Thun 72759925234 8
Wangen an der Aare 15 10 8 12 3
Walenstadt 25 28 46 34
Total 16 101 233 258 237 102 45 10
Percent 1.60 10.08 23.25 25.75 23.65 10.18 4.49 1.00
TABLE II. Number of shots and number of shots above threshold at the 918 receiver points in the sample 共all values represent the yearly average over the
years 2004, 2005, and 2006兲.
Type of weapon/
ammunition
No. of shots
during day
No. of shots
during evening
No. of shots
⬎L
AE
=50 dB
No. of shots
⬎L
AE
=60 dB
No. of shots
⬎L
AE
=70 dB
No. of shots
⬎L
AE
=80 dB
Large caliber 5 088 179 2 119 1 701 834 207
Middle caliber 336 351 11 808 38 141 18 954 17 194 14 699
Small caliber 8 554 533 532 128 303 277 179 902 73 783 0
Practice ammunition 32 650 4 862 0000
Grenades/explosive charges 17 163 1 065 2 356 1 712 816 471
Mortars 6 443 583 1 514 1 271 1 266 737
2304 J. Acoust. Soc. Am., Vol. 127, No. 4, April 2010 M. Brink and J. M. Wunderli: Annoyance from military shooting noise

Using linear regression models, it was first assessed
which exposure metrics appear to be the best predictors of
annoyance. The following potential predictors were investi-
gated: Total energetic and arithmetic average 共over 3 years兲
sound exposure levels 共L
AE
and L
CE
兲, energetic and arith-
metic average sound exposure level 共L
AE
and L
CE
兲 during
day and during evenings, energetic average sound exposure
level 共L
AE
and L
CE
兲 of small caliber shots and of large caliber
shots, total number of small caliber shots over 50 dB L
AE
,
and total number of large caliber shots over 98 dB L
CE
. From
these preliminary analyses, it became evident that the basic
energetic dose measures L
AE
and L
CE
are the best predictors
for shooting noise annoyance. Table
III tabulates the mean
annoyance rating per exposure level category as well as the
percentage of highly annoyed persons 共%HA兲 in each cat-
egory, according to the “standard” cutoff points 共5-point:
60%; 11-point: 72.7%兲 on the scales.
Annoyance is an increasing function of the sound expo-
sure level up to the exposure level category of 115–120 dB
L
AE
. Contrary to expectation, within the higher level catego-
ries 共120–125 and 125–130 dB L
AE
兲, mean annoyance as
well as the percentage of highly annoyed persons 共%HA兲
drop to a level close to the level reported by respondents that
are 15 or even 20 dB less exposed. This could be explained
by some types of self-selection process being at work insofar
as people not being annoyed by military shooting noise are
over-represented in areas close to military shooting grounds,
maybe because they are less sensitive to noise and/or have a
more positive attitude toward the army, e.g., because they are
army employees that live in the vicinity of their employer.
This explanation appears feasible since 共a兲 noise sensitivity
共as measured by the LEFK兲 is a significant negative predictor
of the exposure, as expressed in the L
AE
in linear regression
analysis 关
␤
=−0.11, t共1000兲 = −2.33, p = 0.02兴; 共b兲 annoy-
ance, as measured using the five-point verbal scale, and atti-
tude toward the army 共an index value between 1 and 5 with
higher values denominating a more positive attitude, derived
from items of the questionnaire, see Sec. II B兲 is negatively
correlated within the sample 关r=−0.28; p ⬍ 0.0001兴. 共b兲
Furthermore, in general linear modeling of annoyance 共five-
point verbal scale兲, both L
AE
and attitude independently pre-
dict annoyance 关L
AE
:F共1兲= 94.23, p ⬍ 0.0001; attitude:
F共1兲= 89.64, p ⬍ 0.0001兴, whereas attitude is negatively re-
lated to annoyance in this model.
The annoyance ratings showed considerable variability
as can bee estimated from the confidence intervals reported
in Table
III. Linear regression results of the individual data
共not the grouped data兲 for the 11-point numerical scale
yielded R
2
values of less than 0.05, and the 5-point verbal
scale yielded an adjusted R
2
value of 0.08 for both L
AE
and
L
CE
as predictor. While with transportation noise, on the in-
dividual level, R
2
values between 0.1 and 0.2 are common,
the marginal relationship found with military shooting noise
is no surprise, assuming that individual moderators more
strongly influence the annoyance rating than would be the
case with transportation noise.
TABLE III. Mean annoyance and percent highly annoyed 共%HA兲 for different degrees of exposure. The
categories are defined based on the L
AE
metric, the average exposure values 쏗-L
AE
and 쏗-L
CE
pertain to the
arithmetic average of all cases within the category boundaries. N refers to the number of cases in each exposure
level category.
Level category
共range of L
AE
values兲 Scale Mean annoyance CI −95% CI +95% St. dev. %HA
90–95 共N =16兲 11-point 关0,…,10兴 3.38 2.12 4.63 2.36 6.25
쏗-L
AE
=93.64 5-point 关1,…,5兴 1.81 1.46 2.16 0.66 0.00
쏗-L
CE
=114.87
95–100 共N =101兲 11-point 关0,…,10兴 2.83 2.27 3.40 2.86 7.92
쏗-L
AE
=98.07 5-point 关1,…,5兴 2.10 1.89 2.31 1.05 7.92
쏗-L
CE
=111.50
100–105 共N =233兲 11-point 关0,…,10兴 3.83 3.47 4.19 2.77 10.73
쏗-L
AE
=102.67 5-point 关1,…,5兴 2.41 2.26 2.55 1.12 15.45
쏗-L
CE
=116.37
105–110 共N =258兲 11-point 关0,…,10兴 4.14 3.77 4.51 3.00 16.28
쏗-L
AE
=107.53 5-point 关1,…,5兴 2.53 2.38 2.68 1.20 23.26
쏗-L
CE
=119.66
110–115 共N =237兲 11-point 关0,…,10兴 4.65 4.26 5.03 3.03 22.78
쏗-L
AE
=112.30 5-point 关1,…,5兴 2.97 2.82 3.13 1.24 32.07
쏗-L
CE
=123.77
115–120 共N =102兲 11-point 关0,…10兴 5.35 4.78 5.92 2.91 28.43
쏗-L
AE
=117.32 5-point 关1,…,5兴 3.41 3.18 3.65 1.20 43.14
쏗-L
CE
=129.21
120–125 共N =45兲 11-point 关0,…,10兴 5.09 4.30 5.88 2.63 22.22
쏗-L
AE
=122.21 5-point 关1,…,5兴 3.11 2.78 3.44 1.09 35.56
쏗-L
CE
=131.40
125–130 共N =10兲 11-point 关0…10兴 3.90 1.68 6.12 3.11 10.00
쏗-L
AE
=127.74 5-point 关1,…,5兴 2.60 2.00 3.20 0.84 10.00
쏗-L
CE
=134.09
J. Acoust. Soc. Am., Vol. 127, No. 4, April 2010 M. Brink and J. M. Wunderli: Annoyance from military shooting noise 2305

Frequently asked questions

Q1. What are the contributions in "A field study of the exposure-annoyance relationship of military shooting noise" ?

This article reports a field study on noise annoyance from military shooting with small, midsize, and heavy weapons that was carried out among 1002 residents living near eight different training grounds of the Swiss army. The goal of the study was to derive the exposure-annoyance relationship for military shooting noise in communities in the vicinity of average military training grounds. The inclusion of the C-A frequency weighting difference as a second explaining variable, as suggested earlier, did not substantially enhance the predictability of high annoyance. 

Q2. What is the reason for the inclusion of this second predictor?

The inclusion of this second predictor is based on the idea that for large weapons with considerable low frequency content, the A-weighted level alone does not sufficiently account for the variation in annoyance. 

Q3. What was the main block of questions used?

This main block of questions included the German version of the 11-point annoyance scale from 0 to 10 recommended by the International Commission on Biological Effects of Noise ICBEN that were published by Fields et al.