PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany“Humming” or “Hissing”? Psychoacoustical investigation of sounds from heat pumps
Marc SCHNEIDER1; Carolin FELDMANN2
1

ebm-papst Mulfingen GmbH & Co. KG, Germany
2

University of Siegen, Germany

ABSTRACTHeat pumps, which become increasingly popular as heating systems for houses, with the build-in fan as main
acoustic source could be annoying for the neighborhood.
Previous jury tests with a semantic differential reveal that besides the psychoacoustic loudness and sharpness,temporal structures in a sound signal have a significant impact on the quality evaluation of fan noise. In thiscontext, the blade passing frequency (BPF) and its harmonics play an important role. It emerges, that
distinctive sound patterns rated “helicopter-like” by acoustic experts especially when tonal signatures in thesignal are amplitude modulated with BPF. From a further jury test based on synthetic generated sounds,
which were derived from measured fan sounds in heat pump applications, two different evaluation clusters
with opposing assessments were determined: one major group, which prefers the “hissing of the fan” and asmaller group, which favors the “humming of the electric motor”. In an attached interview some participantsof the test describe a “harmonic balance” of the two mentioned sensations as ideal. By changing the blade
shape of an axial fan, design optimizations should be investigated psychoacoustically. Therefore theannoyance will be predicted based on the previous results and directly measured in a jury test.
Keywords: Jury test, Annoyance, Blade passing frequency, Modulation, Temporal structures

1. INTRODUCTION
Heat pumps are according to the German Association Bundesverband Wärmepumpe e.V. in themeantime the second often requested heating technology for private households. In consequence thenoise emission from these devices constantly increases. Especially the flow noise of the build-in fan
often leads to complaints. Jury tests with the method of the semantic differential showed that besides
the psychoacoustic perception variables loudness and sharpness temporal structures in a noise signal,
characterized by “restiveness” (German: “Unruhe”) or “irregularity” (German: “Ungleichmäßigkeit”),
have a significant impact on quality judgement. Acoustic experts describe a prominent time structureappearing especially for axial fans with a blade passing frequency fBPF < 100 Hz often as “helicopterlike”. Modulation analysis show that these “helicopter-like” sensations occur when tonal signaturesin a sound sample are amplitude modulated with the blade passing frequency fBPF, cp. Figure 1. The
perception of an amplitude modulation or a tone depends on the characteristics of the dominant tonalcomponent levels.
According to Terhardt (1) integer ratios of tones lead to a hardly or even not at all noticeable
temporal structure. This contradicts in the first instance the apparent amplitude modulation ofmultiples of the blade passing frequency with this modulation frequency.
In contrast to the theories of von Helmholtz (2) and Terhardt (1), according to which a welltempered scale leads to a higher consonance, Miskiewicz et al. (3) and Vencovsky and Rund (4) show
by investigating complex tone pairs, that integer frequency ratios can produce a higher subjective
perceived roughness than tone pairs in equal temperament.
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marc.schneider@de.ebmpapst.com
carolin.feldmann@uni-siegen.deThe method of paired-comparison is used to examine the influence of integer tone ratios undervariation of the tone levels and the basic frequency on the preference judgement.

Figure 1 – Degree of modulation over modulation frequency of a “helicopter-like” flow noise
signal. The dominant modulation frequency is equivalent to the blade passing frequency fBPF, which
results from the rotational number times the blade number of the used fan.

2. METHOD
For the investigation of integer tone component ratios under variation of the tone levels and thebasic frequency the fan flow noise is reproduced by a filtered pink noise xn (t) (Butterworth low-passfilter at f = 1,2 kHz) and eight tone components in integer frequency ratios xt (t) according to‫ݔ‬ሺ‫ݐ‬ሻ ൌ ‫ݔ‬௡ ሺ‫ݐ‬ሻ ൅ ‫ݔ‬௧ ሺ‫ݐ‬ሻ଼ൌ ‫ݔ‬௡ ሺ‫ݐ‬ሻ ൅ ෍ ‫ܣ‬௜ ‫ ݊݅ݏ‬ሺʹߨ݂݅௧௢௡௘ ‫ ݐ‬൅ ߮௜ ሻ(1)௜ୀଵwhere the phases φ i of the tones are extracted from a “helicopter-like” fan noise signal.
The levels L T,i of the first three tone components were varied in three steps of 6 dB each. As basis
the Tone-to-Noise Ratio TNR 0 of the BPF from the previously selected “helicopter-like” fan noise
signal is taken and plotted as reference line indicated with „0 dB“ in Figure 2. The tones 4 – 8 are
only be used to make the noise signal sound more voluminous and fuller in order to achieve a highsimilarity to real flow noise signals.

Figure 2 – Narrow-band spectrum of a synthetic flow noise example with maximal cho sen Toneto-Noise Ratio (TNR) of the first three harmonics of BPF. These three harmonics were decreased inthree steps of 6 dB respectively (band width ∆f = 2 Hz, Hanning window with overlap 50 %).

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Two jury tests were performed with the basic tone frequencies fA = 48,5 Hz resp. fB = 76,5 Hz. The
test language is German – therefore the original used adjectives are indicated in brackets behind themost suitable English translation in this paper (German: “x”). Since the noise signals within one
listening test differ just by the tone levels LT,i, the method of paired-comparison is chosen. This method
allows for the detection of small differences of the tested characteristic – in this case the adjective“unpleasant” (German: “unangenehm”). The three steps of three tones result in 27 possiblecombinations. The number of test signals is reduced by the Latin-square method to nine combinations
because a full comparison of all possibilities would exceed the power of concentration of the tes t
persons, cp. Bortz and Schuster (5).
The tested combinations of the tone levels are shown in Table 1. All sound pairs are queried twice
within the jury test and named “Test” (comparison of sound 1 with 2) resp. “Retest” (comparison ofsound 2 with 1). That leads to 72 comparisons all together.
Table 1 – Selection of the nine chosen TNR combinations for the jury tests
with basic frequency fA = 48,5 Hz resp. fB = 76,5 Hz.
LT,1 -TNR0

LT,2 -TNR0

LT,3 -TNR0

10 dB

0 dB0dB

20 dB

-6 dB

-6 dB

30 dB

-12 dB-12 dB

4-6 dB

0 dB

-6 dB

5-6 dB-6 dB-12 dB

6-6 dB-12 dB0 dB

7-12 dB

0 dB-12 dB

8-12 dB-6 dB0 dB

9-12 dB-12 dB-6 dB

Sound No.

For the jury tests all sounds were adjusted to an equal A-weighted sound pressure level of 55 dB(A)and presented to the test persons for a duration of 10 s. The test was controlled by a graphical interface
in Matlab ® . 20 probands each took part in listening test A (50 % male, ᴓ 28 years) resp. B (45 % male,ᴓ 25 years). Seven test persons attended both studies. Here it has been taken care, that approximately
half of the probands started with jury test A and the other half with jury test B. The participants wereinstructed in written form. They were requested to choose in each paired comparison the more
unpleasant sound via a button in the GUI. In addition the test persons were asked to state at least one
word in an implemented comment line why this signal is rated more unpleasant. The sounds werepresented individual in a random order to avoid rank order effects. The first test part was completed
after 36 of the total number of 72 comparisons. Because of the random arrangement of the signals thetwo test parts are not synonymous with “Test” and “Retest”. The second test part was conducted after
a longer interruption (generally at least one day). After completion of the second test part theparticipans were questioned in an interview. They were asked to name pleasant and unpleasant
properties of the sound signal.

3. RESULTS
Whereas the participants in jury test A (fA = 48,5 Hz) judge significant consistent, an equivalentconcordance for jury test B (f B = 76,5 Hz) can’t be found. A hierarchical cluster analysis according to
WARD’s method reveal two clusters B 1 (60 % of the probands) and B 2 (40 % of the probands). The
test persons of the clusters B 1 as well as jury test A evaluate sound no. 1 and no. 4 as most unpleasant,whereas the probands from cluster B2 on the contrary evaluate these sounds as most pleasant.
Participants who attended both jury tests show a consistent judgement behaviour, despite the change
in basis frequency.

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A F-Test shows statistically significant main effects over all three varied BPF tone levels for thejury test A with the basic frequency of 48,5 Hz, cp. Table 2. However, the residual sum of squares
indicates possible interaction effects whereby a reasonable interpretation of the principal effects is
not possible at this point (Bortz and Schuster (5)).
Table 2 – Results of F-test to determine significant main effects by varying theTNR of the three harmonics L T,i from Latin-square method for the jury test A.
A(Test)A (Retest)

F(LT,1)

17,3**

4,3*

F(LT,2)44,6**

39,0**F(LT,3)

55,9**

62,2**FResid

3,88*

5,63**+significant on 10 % levelsignificant on 5 % level** significant on 1 % level*The F-Test is applied to the results of both clusters B1 und B 2 of jury test B, see Table 3. While forcluster B1 a significant main effect for all tone levels L T,i can be found (in the Retest with significant
residual sum of squares), the results of the second cluster B2 show significant effects only for tone
levels L T,2 und L T,3 . Thus, the tone level L T,1 of the basic frequency (fB = 76,5 Hz) reveals no significant
influence on the probands rating.
Table 3 – Results of F-test to determine significant main effects by varying theTNR of the three harmonics L T,i from Latin-square method for the clusters B 1 and B 2.
B1 (Test)

B1 (Retest)

B2 (Test)

B2 (Retest)

F(LT,1)17,2**

3,6*

0,7

0,2

F(LT,2)

15,8**

14,3**

6,4**

2,8+

F(LT,3)

20,7**

12,2**

10,6**

7,6**

FResid2,25

7,19**

0,10

0,47+

significant on 10 % levelsignificant on 5 % level** significant on 1 % level*The median of rank order RO from the paired-comparison is compared to the frequency of mention
h i of the statements in the comment line of the jury test GUI. Therein the highest rank order (1)corresponds to the most annoying sound sample in the test. Plotting the rank order RO over the mostfrequently mentioned term “humming” (German: “Brummen”) show in Figure 3 (left) that a linear
correlation between the perceived “humming” and the evaluation “unpleasant” in the results from theclusters A (r = -0.98, p < 0,01) and B 1 (r = -0.79, p < 0,05) can be found. What is remarkable is thatthe adjective “humming” is used in jury test A four times as often as in test B 1. The sounds no. 3, 5
and 9 are rated less unpleasant by the proband clusters A and B 1 and were hardly described as“humming”. The found trend is confirmed in the subsequent interview, where the participants statethat “humming”, which they assign to the component “motor” leads to a higher annoyance of thesound signal. On the other hand test persons of cluster B2 state that they feel disturbed by the highfrequency of a “hissing” (German: “Rauschen”) sound. The German “Rauschen” is translated by“hissing” here (another option would be “noisy”) because of the fact that the test persons mention
explicitly the high frequency regime in connection with annoyance. This “hissing” is connected to thecomponent “fan” and flow noise. The relation to the term “hissing” is depicted in Fig. 3 (right). Here
only cluster B 2 shows a linear relationship (r = -0.78, p < 0,05). In the interview additional preferences8039emerge besides the two represented by clusters B1 and B 2. While the participants in the jury test prefer
either a “humming” or a “hissing” sound, the attached questionnaire reveals that some of themperceive definitely both phenomena as disturbing. These test persons describe a “harmonic balance”
of the two mentioned sensations as ideal, which means that they merge both phenomena to one sound,so that two different single sounds are no longer existent.

Figure 3 – Median of rank order RO from paired-comparison over the frequency of mention
h humming (left) and h hissing (right) from the named interview statement „humming“ (left) and„hissing“ (right) for jury test A and the clusters B1 and B2 of jury test B. The highest rank order(RO = 1) corresponds to the most annoying sound sample in the test.
Besides the two mentioned terms “humming” and “hissing” the probands use the adjective “roaring”(German: “wummernd”) in jury test A (48,5 Hz) and “buzzing” (German: “summend” and “surrend”)
in jury test B (76,5 Hz). The time structure of the signals is more often the reason for a lower
preference in test A, expressed in adjectives like “restive” (German: “unruhig”) or “irregular”(German: “ungleichmäßig” and “unregelmäßig”). The “humming” and “roaring” is recognized as“moving around the head” from some participants.

4. CONCLUSIONSIn a jury test with the method of paired-comparison the influence of tones with integer frequency
ratio embedded in a synthetic broadband noise signal is investigated with respect to preference. Thisis done by varying the levels of the first three BPF harmonics (derived from measured fan sounds) for
two basic frequencies. While for a low frequency of 48,5 Hz all test persons state that “humming”(German: “Brummen”) leads to higher annoyance of the sound, two opposite judging proband clusters
appear for the basic frequency of 76,5 Hz: 40 % of the test persons prefer humming noise, e.g. a8040

combination of tone levels according to a classical amplitude modulation in comparison to hissing
noise. The test persons associate the attributes “humming” (German: “Brummen”) and “hissing”(German: “Rauschen”) directly with the components “motor” and “fan”. In an attached interview someparticipants of the test describe a “harmonic balance” of the two mentioned sensations as ideal.
Besides “humming” they use “roaring” (German: “Wummern”) for a frequency of 48,5 Hz, at thehigher frequency of 76,5 Hz the term “buzzing” (German: “Summen” and “Surren”). It is notable, thatterms with regard to time structure like “restive” (German: “unruhig”) or “irregular” (German:“ungleichmäßig”) are used more often for the lower basic frequency. The “humming” and “roaring”
is recognized as “moving around the head” (German: „wandernd um den Kopf“) from someparticipants.

REFERENCES
1. Terhardt E. Ein psychoakustisch begründetes Konzept der musikalischen Konsonanz. Acustica, 36(1976). p. 121-137.
2. Helmholtz H v. Die Lehre von den Tonempfindungen. 6th ed. Braunschweig: Friedr. Vieweg & Sohn;
1913.
3. Miskiewicz A, Rakowski A, Roscieszewska T. Perceived Roughness of two simultaneous harmoniccomplex tones. Archives of Acoustics No. 3, 32 (2007). p. 737-748.
4. Vencovsky V, Rund F. Roughness of two simultaneous harmonic complex tones on just-tempered andequal-tempered scales. Music Perception: An Interdisciplinary Journal No. 2, 35 (2017). p. 127 - 143.
5. Bortz J, Schuster C. Statistik für Human- und Sozialwissenschaftler. Berlin/Heidelberg: Springer Verlag;
2010.

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