Technical Notes/JSAE Review 20 (1999) 117—136

Technical Notes

Modification of Booming Level for higher correlationwith booming sensation

Shigeko Hatano, Takeo HashimotoDepartment of Mechanical Engineering, Faculty of Engineering, Seikei University, 3-3-1 Kichijoji Kitamachi, Musashino, Tokyo 180-8633, Japan

Received 25 March 1998

1. Introduction

In our previous study, we proposed a new objectivemeasure, i.e., Booming Level for quantifying boomingsensation caused by car interior noise [1]. In general, thismeasure correlated well with the booming sensation,except in the case where the car interior noise had muchlower frequency components. The poor correlation withthe sound having lower frequency components was dueto the insufficient booming weighting for the low fre-quency components. In the paper, Booming Level wasmodified through a subjective experiment rating boom-ing sensation with sounds having lower frequency com-ponents than 63 Hz for a better fit with the subjectiverating. As a result, the correlation of this modifiedmeasure was highly improved for the sounds having lowprominently frequency components.

2. Booming Level

Booming level was defined in the following form [1]:

Booming ¸evel"0.119]C +i

B(Fci);CUT$B

MB(Fci)]¼(Fci)

]CN/ND](0.0463]¸oudness

#0.397) (BL) (1)

where Fci is the ith center frequency of 1/3 octave bandsfrom 25 Hz to 10 kHz, B(Fci) is the SPL of each 1/3octave band, Cº¹

$B"MmaximumMB(Fci)N!12N50 (dB),

¼(Fci)"2.13]exp(!0.151]X(Fci)), (X(Fci) repres-ents the order of center frequency of 1/3 octave band asX(Fc)"1 when Fc"25 Hz), C"0.046]MB(Fc(i!1))!B(Fci)N#1 (0(B(Fc(i!1))!B(Fci)4g), C"1

(B(Fc(i!1))!B(Fci)40 or B(Fc(i!1))!B(Fci)'9), and N is the number of chosen bands.

The level of this measure is scaled to take 10 (BL) at the1/3 octave band pink noise whose center frequency is63 Hz and whose loudness is equal to 13 sone.

3. Experiment for the modifications of the weightingfunction and B(Fc)

3.1. Experimental stimuli

Sixteen kinds of 1/3 octave band pink noise with25—800 Hz as its center frequency (Fc) were used. Theloudness of the sound was set equal to 13 sone.

3.2. Procedure and subjects

Booming sensations of the sounds presented to thesubject binaurally through a headphone were rated bymagnitude estimation (ME). Each test sound (duration:3 s) was presented to the subject 1.5 s after the referencesound was presented. In view of the frequency spectrum ofcar interior noise, the reference sound chosen was a band-pass pink noise from 90 to 560 Hz. Twenty four subjectsaged between 22 and 51 years with normal hearing abilitytook part in this experiment.

3.3. Modification of the weighting function for 1/3 octaveband noise

The result is shown in Fig. 1. The curve in Fig. 1 repres-ents the previous weighting function obtained from theexperimental result using a set of 1/3 octave band pinknoise with the center frequency above 50 Hz [1]. WhenFc"40 Hz, the booming sensation is the largest and itdecreases as Fc decreases. When Fc is above 40 Hz, the

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0389-4304/99/$19.00 ( 1999 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved.PII: S 0 3 8 9 - 4 3 0 4 ( 9 8 ) 0 0 0 5 2 - 6 JSAE9930207

Fig. 1. Booming sensation for 1/3 octave band pink noise.

Fig. 2. Relation between weighting function ¼(Fc) and B(Fc)]¼(Fc).

Fig. 3. Relation between Booming Level (modified) and ME value forbooming sensation.

result coincides with the curve previously obtained. So wedecided to use the ME values in Fig. 1 for Fcbelow 50 Hz and the previous curve of Fc above 40 Hz forthe new weighting function. The new ¼(Fc) was obtainedby normalizing the above values by dividing the value ofX"5 in Fig. 1.

3.4. Modification of B(Fc)

Fig. 2 shows the Booming Levels calculated by usingthe new ¼(Fc) that are divide by the Booming Level of 1/3octave band pink noise at Fc"63 Hz for 16 stimuli. Theresult should be identical to ¼(Fc). In order to realize thecoincidence of the result with ¼(Fc), B(Fc) in Eq. (1) wasmodified as follows:

B(Fc)"B(Fc)!B(pink63), C"1 for any Fc.

Here B(pink63) means the sound pressure level of 1/3octave band pink noise with Fc"63 Hz. This modifica-

tion was the same as setting the loudness filter at 13 sonefor the better coincidence with subjective results. Therelation between ME values of booming sensation and themodified Booming Level is shown in Fig. 3. The correla-tion coefficient is equal to 0.998, proving a good modifica-tion.

4. Modification of weighting function for various loudness

In our previous paper [1], we obtained the weightingfunction of loudness using the sounds for the threevalues of loudness, i.e., 5, 8 and 13 sone. In this paper,we extended the loudness range of the sounds to extendthe effectiveness of the weighting function for greaterloudness.

4.1. Experiment

The procedure of the experiment was the same as inSection 3. The sound stimuli were the five kinds of artifi-cial sounds which were on the weighting function of loud-ness in our previous paper [1] and two characteristic carinterior noises, that is, one with relatively more boomingsensation and the other with less booming sensation. Thestimuli were presented at six values of loudness, i.e., 5, 8,13, 20, 30 and 40 sone. 22 subjects with normal hearingaged between 22 and 51 years joined in this experiment.

4.2. Modification of the weighting function for various loud-ness

Fig. 4 shows the relation between the loudness andME/ME(13 sone) for the artificial sounds, whereME/ME(13 sone) means ME value divided by ME valueof the same sound with its loudness of 13 sone. The curvein Fig. 4 is represented by the polynomial of degree2 (½(loudness)) obtained by the method of least-square

124 Technical Notes / JSAE Review 20 (1999) 117—136

Fig. 4. Relation between loudness and ME/ME(13 sone).

Fig. 5. Relation between Booming Level (modified) with ½ and MEvalue for booming sensation.

Fig. 6. Relation between Booming Level (modified) with ½ and boom-ing factor score.

approximation. The result obtained by using ½(loudness)is shown in Fig. 5. The correlation coefficient becomes0.838 which is a little higher than that (r"0.817) obtainedby using (0.0463]Loudness#0.397) in Eq. (1).

5. Booming factor score and modified Booming Level

An experiment of rating 11 kinds of car interior noise bysemantic differentials was carried out using 10 pairs ofadjectives, i.e. soft—hard, clamorous—quiet, deep—metallic,clear—sonant, strong—weak, booming—ringing, har-monic—discordant, pleasant—unpleasant, powerful—un-satisfactory, flat—rumbling. According to the result offactor analysis, the third factor was related to the boomingsensation. Fig. 6 shows the relation between the boomingfactor scores and the modified Booming Level with ½. Thecorrelation is high, and we could prove the usefulness ofthe modified Booming Level as a better measure forbooming sensation.

6. Conclusions

1. It is shown that booming sensation takes maximumvalue at Fc"40 Hz from the result of the experiment onbooming sensation using 1/3 octave band pink noise with25—800 Hz as its center frequency.

2. Booming Level was modified with the new weightingfunction for booming sensation and the modified 1/3 oc-tave band level. The correlation between the modifiedBooming Level and the rating of the booming sensation isimproved significantly with the sounds having much lowerfrequency components.

References

[1] Hatano, S. and Hashimoto, T., On an objective measure of thebooming sound factor — modification of the measure for the spec-trum pattern and the loudness of the sound, (in Japanese withEnglish summary), Trans. JSAE, Vol. 27, No. 2, pp. 85—89 (1996).

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