PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

New single-number quantities for evaluation ofimpact sound insulation
Mikko KYLLIÄINEN1; Petra VIRJONEN2; Valtteri HONGISTO212

Tampere University, Finland

Turku University of Applied Sciences, Finland

ABSTRACTThe standardized single-number quantities for evaluation of impact sound insulation do not correlate
especially well with the subjective judgment of living impact sound sources directed to the floors. The aimof this study was to find new single-number quantities better associated with the subjective annoyance causedby diơerent impact sounds. The new single-number quantities were developed on the bases of experimental
data of laboratory measurements of impact sound insulation of floors and a psychoacoustic experiment. Five
impact sound types were studied: walking with hard shoes, socks, and soft shoes, super ball bouncing, andchair moving. Basic requirement was that the new single-number quantities could be expressed as the sumof L’n,w or L’nT,w and new spectrum adaptation terms. Reference spectra for calculation of new spectrum
adaptation terms for each sound type were derived by the means of a mathematical optimization method. Inaddition, an optimized reference spectrum based on all five sound types was derived. An optimized reference
spectrum based on all five sound types explained the annoyance of the five sound types reasonably well.
Keywords: building acoustics, impact sound insulation, single-number quantity

1. INTRODUCTION
It has been long recognized (1–5) that the single-number quantities (SNQ) presented in the standard
ISO 717-2 (6) do not correlate especially well with the subjective judgment of living impact soundsources directed to the floors. There have been two strategies for solving the problems. Firstly,
modifying or replacing the standard tapping machine as a sound source has been suggested. There is,however, some evidence indicating that the alternative sound sources to the tapping machine do notnecessarily lead into a better association between the objective SNQs and subjective rating (7). The
second strategy for solving the problematics concerning the association between the SNQs andsubjective rating is defining a new SNQ based on the tapping machine as a sound source (8). Several
alternative SNQs for rating the impact sound insulation of floors have been suggested since the 1960s(2, 9–12).
A recent psychoacoustic experiment dealing with the impact sound insulation of concrete floors
indicated that the standardized SNQs, L’ n,w, L’ n,w + C I and L’ n,w + CI,50-2500 were not always wellassociated with subjectively perceived loudness or annoyance of different impact sound sources (13).
This concerns also the four alternative SNQs (2, 10–12).
The aim of the study reported in this paper was to develop alternative SNQs for impact soundinsulation that explain well the annoyance caused by various impact living sounds transmitted fromthe neighboring dwelling upstairs. Alternative SNQs concern five spectra lly different impact sounds(walking with hard shoes, walking with socks, walking with soft shoes, superball bouncing, chairmoving) experimentally investigated in (13). The object also was to develop a SNQ that explains well
the annoyance caused by all five impact living sounds. This paper is based on a wider study reported
in the reference (14).
12mikko.kylliainen@tuni.fi
forename.surname@turkuamk.fi

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2. MATERIALS AND METHODS
2.1 Basic Requirements
It seems obvious that the tapping machine will remain as the primary impact sound source (15).
Therefore, it was assumed that a new method for rating the impact sound insulation could be foundby deriving a better SNQ or reference curve instead of replacing the tapping machine with some othersound source, such as Japanese ball used in ISO 16283-2 (16). In addition, basic requirement was thatthe new single-number quantities could be expressed as the sum of L’ n,w or L’ nT,w and new spectrum
adaptation terms. The alternative SNQs are developed for the frequency range 50–2500 Hz.
2.2 Experimental Data
The experimental data utilized in the study originates from a psychoacoustic laboratory experimentconcerning subjective loudness and annoyance of different impact sounds. The conduction of thepsychoacoustical experiment has been reported in the reference (13). The recording of living impact
sounds and measurements of the impact sound insulation of different floors has been reported in thereference (17).
The experiment involved 45 impact sounds. They were created by recording sounds of fivedifferent impact sound sources directed to nine different floor types in an impact sound insulationlaboratory. The floor types consisted of nine floor constructions: a bare 265 -mm-thick hollow coreconcrete slab (F1) and eight different floor coverings (F2–F9) installed on the top of F1. The
normalized impact sound levels L’ n [dB] were measured according to ISO 140-7 (18) using the tapping
machine. The floor coverings and the impact sound insulation measurements have been described indetail in the reference (17). The floor coverings of constructions F2–F9 were:-F2: hard cushion vinyl (ΔLw = 2 dB),F3: soft cushion vinyl ΔL w = 21 dB),
F4: parquet and soft underlayment ΔL w = 20 dB),
F5: hard wall-to-wall textile carpet (ΔL w = 21 dB),F6: soft wall-to-wall textile carpet (ΔL w = 37 dB),
F7: F4 on top of a floating floor 1 (2 plasterboards and 13 mm mineral wool) ΔLw = 29 dB),
F8: F4 on top of a floating floor 2 (2 plasterboards and 50 mm mineral wool) ΔLw = 36 dB),
F9: F4 on top of a floating floor 3 (4 plasterboards and 50 mm mineral wool) ΔLw = 38 dB).

In the impact sound insulation laboratory, five different impact sound types S1–S5 were recorded
in for each floor type F1–F9. The sound types were:-S1: walking with hard shoes
S2: walking with socks
S3: walking with soft shoes
S4: super ball bouncing
S5: chair moving

There were fifty-five voluntary people (25 male, 30 female) participating in the experiment. Theirage varied between 20 and 57 years. The impact sounds were played from several loudspeakers
installed above the suspended ceiling so that the impact sounds seemed natural. The participants
judged the annoyance of each impact sound. The judgment for annoyance was given on a scale from0 to 10, value 10 indicating that the sound is “extremely annoying” and 0 “not at all annoying because
the sound could not be heard”. The mean values of subjective annoyance (Figure 1) as a subjective
variable were used in the optimization problem since annoyance is closely related to health effects ofnoise and acoustic comfort. The measured normalized impact sound pressure levels L’ n are shown inFigure 2.

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109S1S2S3S4S5Mean

8Annoyance

76543210F1F2F3F4F5F6F7F8F9Floor typeFigure 1 – Mean values of subjective annoyance for each combination of impact sound types S1–S5 andfloor types F1–F9. In addition, the mean over all five sound types (Mean) is shown. The variable on the Xaxis is categorical. Lines are used to facilitate the reading of data.

80706040302010F1F2F3F4F5F6F7F84000

2000

f [Hz]

1000

500

63250

F90125L'n [dB]

50

Figure 2 – Measured normalized impact sound pressure levels L’n of the nine floor types F1–F9.

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2.3 Mathematical Optimization
Mathematical optimization was used to solve our problem instead of using sophisticated guessmethod although both methods may end up to very similar outcomes. Reference spectra for calculationof new spectrum adaptation terms for each sound type were derived by the means of a mathematicaloptimization method. In addition, an optimized reference spectrum based on all five sound types wasderived. Virjonen et al. (19) have already developed optimized reference spectra for airborne soundinsulation by applying mathematical optimization to experimental data presented in the reference (20).
The mathematical optimization method is an effective and quick method for the derivation of ascientifically justified SNQ.
The formulation of the optimization is presented in detail in the reference (14). The subjective
variable for each floor type and sound type was defined as the mean of the ratings of annoyance givenby the 55 participants. It was assumed that the subjective variable depends linearly on the SNQ.
The goal was to find an optimal reference spectrum for each impact sound type S1–S5. The
optimized reference spectrum for impact sound type S1 was called LS1 . For each impact sound type,such a reference spectrum was sought, that the subjective annoyance had the best achievable least squares fit with the resulting SNQs. The optimal reference spectrum was determined by formulating
the problem as a non-linear optimization problem with constraints, and solving it numerically.
The optimized SNQ can be expressed as a sum of the weighted normalized impa ct SPLs L’ n,w anda spectrum adaptation term. E.g. spectrum adaptation term for impact sound S1, CI,S1, can be expressedas଴ǡଵሺ௅ೄభǡೕ ି଻଼ǡଶିଵ଴୪୥௙ೕ ା௅౤ǡೕ ሻെ ͳͺǡͻ െ ‫ܮ‬Ԣ୬ǡ୵‫୍ܥ‬ǡୗଵ ൌ ͳͲ σ௄௝ୀଵ ͳͲ(1)In addition to sound type optimized reference spectra derived above, an optimized reference
spectrum over all five sound type was also derived. This is meaningful since the construction
performances are declared using a single SNQ which is expected to represent all impact sound ty pes
sufficiently well. The optimized reference spectrum was called Lopt and the SNQ calculated from it
L’ n,w + C I,opt. This reference spectrum was derived by adding all 45 experimental sounds (9 floor typestimes 5 sound types) into the same pool.

3. RESULTS
The optimized reference spectra are presented in Fig. 3. The squared correlation coefficients
between the standardized and optimized SNQs and the mean annoyance are given in Table I.
Table 1 – Squared Pearson’s correlation coefficients r2 of the optimized and standardized SNQs for each
impact sound type S1…S5. The best acquired value per sound type is underlined.

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SNQ

S1S2S3S4S5L’n,w + CI,S10,930,380,750,350,73L’n,w + CI,S20,410,870,300,010,31L’n,w + CI,S30,910,350,770,420,69L’n,w + CI,S40,870,240,710,560,59L’n,w + CI,S50,750,260,610,200,87L’n,w + CI,opt

0,920,400,750,350,74L’n,w0,680,090,540,300,80L’n,w + CI

0,830,170,680,440,75L’n,w + CI,50-2500

0,820,270,650,290,82

Figure 3 – The sound type optimized reference spectra LS1…LS5 for the impact sound types S1–S5 (panelsa–e) and the optimized reference spectrum Lopt for all sound types S1–S5 (panel f).

4. DISCUSSION
The standardized SNQs L’ n,w, L’ n,w + C I and L’ n,w + C I,50-2500 correlated relatively well withannoyance for sound types S1 (walking with hard shoes), S3 (walking with soft shoes) and S5 (chairmoving). The correlation was poor for sound types S2 (walking with socks) and S4 (super ballbouncing).
An optimized reference spectrum yielding a high correlation with annoyance could be derived foreach sound type S1–S5. Compared with the SNQs presented in the standard ISO 717 -2 (6), each
optimized reference spectrum produced a higher squared correlation coefficient between theoptimized SNQ and annoyance. Virjonen et al. (19) developed optimized SNQs for airborne soundinsulation using the same mathematical method and the resulting SNQs also explained annoyancemuch better than any of the standardized SNQs. This shows that the mathematical optimization is aconsistent and justified method in striving for SNQs associating the physical measurement results tothe subjective experience of the impact or other sounds.
Walking with socks (sound type S2) is among the most important residential impact sounds (7, 17,20). Thus, the standardized SNQ should be well associated with the annoyance of this sound type.
None of the studied standardized SNQs correlated well with the experienced annoyance of walkingwith socks.
A reference spectrum with a high correlation with annoyance also for sound type S2 (walking withsocks) could be found using the optimization method because this sound type is among the mostprevalent neighbor sounds in residential environments (22). The squared correlation coefficient 0.87
was significantly higher than those of the standardized SNQs L’ n,w , L’ n,w + C I and L’ n,w + CI,50-2500 (r2values within 0.09–0.27). All the sound type optimized reference spectra gave better squared
correlation coefficients than any of the standardized SNQs.

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The optimized reference spectrum for sound type S4 (super ball bouncing) produced a better
correlation (r 2 = 0.56) than the standardized single-number quantities L’ n,w , L’ n,w + C I and L’ n,w + C I,502500 . The squared correlation of sound type S4 is, however, clearly lower than for the other sound types.
One reason might be the narrow spread of annoyance responses. However, this cannot be the only
reason since equally narrow spread was observed also for sound types S2 and S3. The reason for lowcorrelation seems to be floor type F6 involving a very soft wall-to-wall carpet. It produces a low SNQ
value but the sound type S4 is judged quite annoying. The soft wall-to-wall carpet leads to the lowest
SPLs from walking (S1–S3) and chair moving (S5), but S4 is an exception. This sound type S4 withwall-to-wall carpet generates similar impact sound spectrum as this sound type with floors F1 –F5 (17)which explains this exception.
It was found important to derive a single reference spectrum that would explain the annoyance
responses reasonably for all five sound types simultaneously. Therefore, an optimized reference
spectrum, Lopt was derived to predict the annoyance of all five sound types. According to Table I, theoptimized reference spectrum is relatively good since it produced higher r2 values than any of thestandardized SNQs for sound types S1–S3. The values were also reasonably high for sound types S4–
S5. Thus, the reference spectrum serves the original purpose of being better than any of thestandardized SNQs.

5. CONCLUSIONS
Reference spectra for rating impact sound insulation of floors were derived by the means of amathematical optimization method. An optimized reference spectrum could be developed for each fivesound types. Each of them correlates better with the subjective annoyance of the impact sounds thanany of the single-number quantities presented in the standard ISO 717-2 (6). In addition, an optimized
reference spectrum could be derived which explained the annoyance of all f ive sound types reasonably
well.

ACKNOWLEDGEMENTS
This study was based on the materials produced during the research project “User-oriented
development of sound insulation in buildings ÄKK” (2012–2014) funded by Tekes – the Funding
Agency for Technology and Innovation (Grant Nos. 2296/31/11, 2297/31/11, 2298/31/11), Ministryof Environment (YM36/612/2012) and eight companies of building industry. Thanks are also due tothe steering group of ÄKK.

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