Some facts on sound waves, sources and hearing
1.7 Sound sources
Sound waves, sources and hearing 27 However, if the sound source is situated within the vertical symmetry plane, this explanation fails since then the source produces equal sound signals at both ear canals. But even then the ear transfer functions show characteristic differences for various elevation angles of the source, and it is commonly believed that the way in which they modify a sound signal enables us to distinguish whether a sound source is behind, above or in front of our head.
These considerations are valid only for the localisation of sound sources in a free sound field. In a closed room, however, the sound field is made up of many sound waves propagating in different directions, and accord- ingly, matters are more complicated. We shall discuss the subjective effects of more complex sound fields as they are encountered in room acoustics in Chapter 7.
Figure1.7Amplitudespectrumandtimefunction(soundpressure)ofvowels/i/(left),/a/(middle)and/u/(right)(afterFlanagan
Sound waves, sources and hearing 29
Figure 1.8 Long-time power spectrum of continuous speech 30 cm from the mouth (after Flanagan5).
which plots the long-time power spectrum of continuous speech, both for male and female speakers.5 The high-frequency energy is mainly due to the consonants, for instance to fricatives such as|s|or|f|, or to plosives such as
|p|or|t|. Since consonants are of particular importance for the intelligibility of speech, a room or hall intended for speech, as well as a public address system, should transmit the high frequencies with great fidelity. The trans- mission of the fundamental vibration, on the other hand, is less important since our hearing is able to reconstruct it if the sound signal is rich in higher harmonics.
Among musical instruments, large pipe organs have the widest frequency range, reaching from 16 Hz to about 9 kHz. (There are some instruments, especially percussion instruments, which produce sounds with even higher frequencies.) The piano follows, having a frequency range which is smaller by about three octaves, i.e. by nearly a decade. The frequencies of the remain- ing instruments lie somewhere within this range. This is true, however, only for the fundamental frequencies. Since almost all instruments produce higher harmonics, the actual range of frequencies occurring in music extends still further, up to about 15 kHz. In music, unlike speech, all frequencies are of
almost equal importance, so it is not permissible deliberately to suppress or to neglect certain frequency ranges. On the other hand, the entire frequency range is not the responsibility of the acoustical engineer. At 10 kHz and above the attenuation in air is so dominant that the influence of a room on the propagation of high-frequency sound components can safely be neglected.
At frequencies lower than 50 Hz geometrical considerations are almost use- less because of the large wavelengths of the sounds; furthermore, at these frequencies it is almost impossible to assess correctly the sound absorption by vibrating panels or walls and hence to control the reverberation. This means that, in this frequency range too, room acoustical design possibilities are very limited. On the whole, it can be stated that the frequency range rel- evant to room acoustics reaches from 50 to 10 000 Hz, the most important part being between 100 and 5000 Hz.
The acoustical power output of the sound sources as considered here is relatively low by everyday standards. Table 1.1 lists a few typical data.
The human voice generates a sound power ranging from 0.001µW (whis- pering) to 1000 µW (shouting), the power produced in conversational speech is of the order of 10 µW, corresponding to a sound power level of 70 dB. The power of a single musical instrument may lie in the range from 10 µW to 100 mW. A full symphony orchestra can easily generate a sound power of 10 W in fortissimo passages. It may be added that the dynamic range of most musical instruments is about 30 dB (woodwinds) to 50 dB (string instruments). A large orchestra can cover a dynamic range of 100 dB.
An important property of the human voice and musical instruments is their directionality, i.e. the fact that they do not emit sound with equal intensity in all directions. In speech this is because of the ‘sound shadow’
cast by the head. The lower the sound frequency, the less pronounced is the reduction of sound intensity by the head, because with decreasing frequencies the sound waves are increasingly diffracted around the head.
Table 1.1 Sound power and power level of some sound sources (the data of musical instruments are for fortissimo)
Source or signal Sound power (mW) Sound power level (dB)
Whisper 10−6 30
Conversational speech 0.01 70
Human voice, maximum 1 90
Violin 1 90
Clarinet, French horn 50 107
Trumpet 100 110
Organ, large orchestra 104 130
Sound waves, sources and hearing 31 In Figs 1.9a and 1.9b the distribution of the relative pressure level for different frequency bands is plotted on a horizontal plane and a vertical plane, respectively. These curves are obtained by filtering out the respec- tive frequency bands from natural speech; the direction denoted by 0◦is the frontal direction.
Musical instruments usually exhibit a pronounced directionality because of the linear dimensions of their sound-radiating surfaces, which, in the interest of high efficiency, are often large compared with the wavelengths.
Unfortunately general statements are almost impossible, since the directional distribution of the radiated sound changes very rapidly, not only from one frequency to the other; it can be quite different for instruments of the same sort but different manufacture. This is true especially for string instruments, the bodies of which exhibit complicated vibration patterns, particularly at higher frequencies. The radiation from a violin takes place in a fairly uniform way only at frequencies lower than about 450 Hz; at higher frequencies, however, matters become quite involved. For wind instruments the direc- tional distributions exhibit more common features, since here the sound is not radiated from a curved anisotropic plate with complicated vibration pat- terns but from a fixed opening which is very often the end of a horn. The
‘directional characteristics of an orchestra’ are highly involved, but space is too limited here to discuss this in detail. For the room acoustician, however, it is important to know that strong components, particularly from the strings but likewise from the piano, the woodwinds and, of course, from the tuba, are radiated upwards. For further details we refer to the exhaustive account of J. Meyer.6
In a certain sense, the sounds from natural sources can be considered as statistical or stochastic signals, and in this context their autocorrelation function is of interest as it gives some measure of a signal’s ‘tendency of con- servation’. Autocorrelation measurements on speech and music have been performed by several authors.7,8Here we are reporting results obtained by Ando, who passed various signals through an A-weighting filter and formed their autocorrelation function according to eqn (1.38b) with a finite inte- gration time of T0 =35 s. Two of his results are depicted in Fig. 1.10.
A useful measure of the effective duration of the autocorrelation function is the delayτe, at which its envelope is just one-tenth of its maximum. These values are indicated in Table 1.2 for a few signals. They range from about 10 to more than 100 ms.
The variety of possible noise sources is too large to discuss in any detail.
A common kind of noise in a room is sound intruding from adjacent rooms or from outside through walls, doors and widows, due to insufficient sound insulation. A typical noise source in halls is the air conditioning system; some of the noise produced by the machinery propagates in the air ducts and is radiated into the hall through the air outlets.
Figure 1.9 Directional characteristics of speech sounds for two different frequency bands.
The arrow points in the viewing direction: (a) in the horizontal plane; (b) in the vertical plane.
Sound waves, sources and hearing 33
Figure 1.10 Examples of measured autocorrelation functions: (a) music motif A; (b) music motif B (both from Table 1.2) (after Ando8).
Table 1.2 Duration of autocorrelation functions of various sound signals (after Ando8)
Motif Name of piece Composer Durationτe, (ms)
A Royal Pavane Gibbons 127
B Sinfonietta opus 48, 4th movement (Allegro con brio)
Arnold 43
C Symphony No. 102 in B flat major, 2nd movement (Adagio)
Haydn 65
D Siegfried Idyll; bar 322 Wagner 40
E Symphony KV 551 in C major (Jupiter), 4th movement (Molto allegro)
Mozart 38
F Poem read by a female Kunikita 10
References
1 Bracewell RN. The Fourier Transform and its Applications. Singapore: McGraw- Hill, 1986.
2 Zwicker E, Fastl H. Psychoacoustics—Facts and Models. Berlin: Springer-Verlag, 1990.
3 Blauert J. Spatial Hearing. Cambridge, Mass: MIT Press, 1997.
4 Flanagan JJ. Speech communication. In: Crocker MJ (ed.), Encyclopedia of Acoustics. New York: John Wiley, 1997.
5 Flanagan JJ. Speech Analysis Synthesis and Perception. Berlin: Springer-Verlag, 1965.
6 Meyer J. Acoustics and the Performance of Music. Berlin: Springer-Verlag, 2008.
7 Furdujev V. Evaluation objective de l’acoustique des salles. Proc Fifth Intern Congr on Acoustics, Liege, 1965, p 41.
8 Ando YJ. Subjective preference in relation to objective parameters of music sound fields with a single echo. Acoust Soc Am 1977; 62:1436. Proc of the Vancouver Symposium (Acoustics and Theatres for the Performing Arts) Canadian Acoust Association, Ottawa, Canada, 1986, p 112.