Introduction to Acoustics

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810 Part F Biological and Medical Acoustics Part F 20.1 20° 40° 60° dB 0 –10 –20 –30 –20° –40° 120 kHz –60° 60 kHz 80° 30 kHz 100° –80° –100° (T. truncatus) H 31 TI 18 20° 40° 60° dB 0 –10 –20 –30 –20° –40° 30 kHz 60 kHz 120 kHz –60° 80° 100° –80° –100° (T. truncatus) H 31 TI 18 Fig. 20.4 Receive beam patterns in the vertical and horizontal planes for frequencies of 30, 60 and 120 kHz. The relative masked thresholds as a function of the elevation angle of the asking noise source are plotted for each signal frequency (after Au and Moore, [20.28]) line with the bite plate and its acoustic output was held constant. Masked thresholds were measured for different angular position of the noise transducer along the arc. The level of the noise was varied in order to obtain the masked threshold. A threshold estimate was considered complete when at least 20 reversals (10 per session) at a test angle had been obtained over at least two consecutive sessions, and if the average reversal values of the two sessions were within 3 dB. After a threshold estimate was achieved, the noise transducer was moved to a new azimuth over a set of randomly predesignated azimuths. As the azimuth about the dolphin’s head increased, the hearing sensitivity of the dolphin tended to decrease, requiring higher levels of masking noise from a transducer located at that azimuth to mask the signal from a source located directly ahead of the animal. The receiving beam patterns in both the vertical and horizontal plane are plotted for signal frequencies of 30, 60 and 120 kHz in Fig. 20.4. The radial axis of Fig. 20.4 represents the difference in dB between the noise level needed to mask the test signal at any azimuth and the minimum noise level needed to mask the test signal at the azimuth corresponding to the major axis of the vertical beam. The shape of the beams in Fig. 20.4 indicates that the patterns were dependent on frequency, becoming narrower, or more directional as the frequency increased. The beam of a planar hydrophone also becomes narrower as frequency increases. The 3 dB beam widths were approximately 30.4 ◦ ,22.7 ◦ , and 17.0 ◦ for frequencies of 30, 60, and 120 kHz, respectively. There was also an asymmetry between the portion of the beam above and below the dolphin’s head. The shape of the beams dropped off more rapidly as the angle above the animal’s head increased than for angles below the animal’s head, indicating a more rapid decrease in the animal’s hearing sensitivity for angles above the head than for angles below the head. If the dolphin receives sounds through the lower jaw, the more rapid reduction in hearing sensitivity for angles above the head may have been caused by shadowing of the received sound by the upper portion of the head structure including air in the nasal sacs [20.29]. There is a slight peculiarity in the 60 kHz beam which shows almost the same masked threshold values for 15 ◦ and 25 ◦ elevation angles. The radial line passing through the angle of maximum sensitivity is commonly referred to as the major
axis of the beam. The major axis of the vertical beams is elevated between 5 ◦ and 10 ◦ above the reference axis. The 30 and 120 kHz results show the major axis at 10 ◦ while the 60 kHz results showed the major axis at 5 ◦ . It will be shown in a later section that the major axis of the received beam in the vertical plane is elevated at approximately the same angle as the major axis of the transmitted beam in the vertical plane. In the horizontal beam pattern measurement, two noise sources were fixed at azimuth angles of ±20 ◦ . The level of the noise sources was also fixed. The position of the signal transducer was varied from session to session. Masked thresholds were determined as a function of the azimuth of the signal transducer, by varying the signal level of the signal transducer in a staircase fashion. A threshold estimate was considered completed when at least 20 reversals at a test angle had been obtained over at least two consecutive sessions, if the average reversal values were within 3 dB of each other. After a threshold estimate was determined, the signal transducer was moved to a new azimuth over a set of randomly predesignated azimuths. Two noise sources were used in order to discourage the dolphin from internally steering its beam in the horizontal plane. If the animal could steer its beam, it would receive more noise from one of the two hydrophones, and therefore not experience any improvement in the signal-to-noise ratio. The masking noise from the two sources was uncorrelated but equal in amplitude. The radial axis represents the difference in dB between the signal level at the masked threshold for the various azimuths and the signal level of the masked threshold for 0 ◦ azimuth (along the major axis of the horizontal beam). The horizontal receiving beams were directed forward with the major axis being parallel to the longitudinal axis of the dolphin. The beams were nearly symmetrical about the major axis. Any asymmetry was within the margin of experimental error involved in estimating the relative thresholds. The horizontal beam patterns exhibited a similar frequency dependence as the vertical beam patterns, becoming narrower or more directional as the frequency increased. The 3 dB beam widths were 59.1 ◦ , 32.0 ◦ , and 13.7 ◦ for frequencies of 30, 60, and 120 kHz, respectively. Zaytseva et al. [20.30] measured the horizontal beam pattern of a dolphin by measuring the masked hearing threshold as a function of azimuth. Their beam width of 8.2 ◦ for a frequency of 80 kHz was much narrower than the 13.7 ◦ for a frequency of 120 kHz. The difference in beam width is even larger if the results of Au and Moore [20.28] are linearly interpolated to 80 kHz. Cetacean Acoustics 20.1 Hearing in Cetaceans 811 We calculated an interpolated beam width of 25.9 ◦ at 80 kHz, which was considerably greater than the 8.2 ◦ obtained by Zaytseva et al. [20.30]. The difference in beam width measured by Zaytseva et al. and Au and Moore may be attributed to the use of only one noise source by Zaytseva et al. compared to the two noise sources used by Au and Moore. With a single masking noise source in the horizontal plane, there is the possibility of the animal performing a spatial filtering operation by internally steering the axis of its beam in order to maximize the signal-to-noise ratio. Another possibility is that Zaytseva et al. did not use a fixed stationing device. Rather, the dolphin approached the signal hydrophone from a start line, always oriented in the direction of the signal hydrophone. The animal responded to the presence or absence of a signal by either swimming or not swimming to the hydrophone. In such a procedure, it is impossible to control the orientation of the animal’s head with respect to the noise masker so that the dolphin could move its head to minimize the effects of the noise. Directivity Index The directivity index is a measure of the sharpness of the beam or major lobe of either a receiving or transmitting beam pattern. For a spherical coordinate system, the directivity index of a transducer is given by the equation [20.31] DI = 10 log 2π � π/2 � 0 −π/2 � p(θ,φ) p0 4π . (20.1) �2 sin θ dθ dφ Although the expression for directivity index is relatively simple, using it to obtain numerical values can be quite involved unless transducers of relatively simple shapes (cylinders, lines and circular apertures) with symmetry about one axis is involved. Otherwise, the beam pattern needs to be measured as a function of both θ, and φ. This can be done by choosing various discrete values of θ and measuring the beam pattern as a function of φ, a tedious process. Equation (20.1) can then be evaluated by numerically evaluating the double integral with a digital computer. The directivity indices associated with the dolphin’s beam patterns in Fig. 20.4 were estimated by Au and Moore [20.28] using (20.1) and a twodimensional Simpson’s 1/3-rule algorithm [20.32]. The results of the numerical evaluation of are plotted as a function of frequency in Fig. 20.5. DIs of 10.4, 15.3 and 20.6 dB were obtained for frequencies of 30, 60, Part F 20.1
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Springer Handbook of Acoustics
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Springer Handbook of Acoustics Thom
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Foreword The present handbook cover
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List of Authors Iskander Akhatov No
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Philippe Roux Université Joseph Fo
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XIV Contents 3.7 Attenuation of Sou
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XVI Contents 10 Concert Hall Acoust
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XVIII Contents 17.8 Physical Modeli
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XX Contents 24.5 Free-Field Microph
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XXII List of Abbreviations K KDP po
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Introduction 1. Introduction to Aco
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of noise have been the subject of c
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in order to understand how objectiv
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A Brief 2. A Brief History of Acous
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of 350 m/s for the speed of sound [
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number and relative strength of its
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To his contemporaries, Koenig was p
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Probably the most important use of
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piezoelectric ceramic compositions
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surveys together [2.46]. Masking of
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ther of computer music, since he de
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Basic 3. Linear Basic Linear Acoust
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M average molecular weight n unit v
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a) b) S v.n ∆t ∆S V |v| ∆t n
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temperature, q =−κ∇T , (3.16)
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The equivalent density M/V is conse
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Basic Linear Acoustics 3.3 Equation
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Because any vector field may be dec
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The latter and (3.84), in a manner
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assumed to have no ambient motion,
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Because the friction associated wit
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3.5 Waves of Constant Frequency One
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3.5.4 Time Averages of Products Whe
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as well as symmetry considerations,
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The auxiliary internal variables th
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Then the transient at a distant pos
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ω ′ = 0, and this is consistent
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1.0 10 -1 10 -2 10 -3 10 -4 10 -5 A
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This yields the interpretation that
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direction of propagation when a pla
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so the time-averaged incident energ
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Although the simple result of (3.31
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ut, also in keeping with the linear
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equation, the two differential equa
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Rodrigues relation, one has �1
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for the derivative.) In the asympto
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The differential scattering cross s
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elow) is F(t) = (2c) 1/2 �t −
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0.5 0 -0.5 -1.0 -1.5 0 Y0(η) (π/2
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is the Wronskian for the Bessel and
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The function qS is termed the sourc
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The appropriate identification for
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where jℓ is the spherical Bessel
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this subtlety taken into account, o
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U(x) Basic Linear Acoustics 3.15 Wa
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is ordinarily valid. With these ass
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along rays. These can be regarded a
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A(x0) x0 A(x) Fig. 3.53 Sketch of a
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possible, and one where neither the
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which is independent of the z-coord
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[3.108], and Carslaw [3.109]. In th
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where C(X)andS(X) are the Fresnel i
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Fig. 3.60 Characteristic diffractio
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of elastic solids, Trans. Camb. Phi
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3.101 J.B. Keller: Geometrical acou
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114 Part A Propagation of Sound Par
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Underwater 5. Underwater Acoustics
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5.1 Ocean Acoustic Environment The
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Long-Range Propagation Paths Figure
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tal direction, there is no loss ass
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equivalent circuit, as shown in Fig
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Attenuation á (dB/km) 1000 100 10
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5.2.5 Ambient Noise There are essen
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ubble natural acoustic resonance ω
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a bubbly medium (and for the simple
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As discussed, because detection inv
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(1/A)∇ 2 A ≪ K 2 )sothat(5.34)
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water, where the deep sound channel
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egion in the form p(r, z) = ψ(r, z
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5.4.6 Propagation and Transmission
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tegration interval. The source puls
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5.6 SONAR Array Processing Signal p
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former output is: �∞ b(θ,t) =
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Fig. 5.37 Angle-versus-time represe
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5.7 Active SONAR Processing Depth M
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a factor when there is a reverberan
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depth measurements that correspond
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along the cross-shelf track taken b
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time as a result of multiple paths,
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technique is very sensitive, and ex
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Fig. 5.57a,b Typical echogram obtai
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Frequency (Hz) 150 100 50 0 0 a) b)
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out. These data allow for study of
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5.59 G. Raleigh, J.M. Cioffi: Spati
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Physical 6. Physical Acou Acoustics
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where I is the intensity of the sou
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Wave velocity The wall exerts a dow
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destructively interfered with one a
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or: � � p2 � rms SPL = 10 log
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6.1.4 Wave Propagation in Solids Si
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where c is again the wave speed and
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measured. Some resonances are cause
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as 50 µmto5µm through one oscilla
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the number of false positives and m
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with the small mass), and frequency
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Laser Lens 1 Circular aperture Fig.
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Ground ring Insulator Sample Resist
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Energy ratio 1.0 0.8 0.6 0.4 Calcul
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terms. In this equation γ is the r
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directly. The nonlinearity paramete
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Thermoacoust 7. Thermoacoustics The
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Table 7.1 The acoustic-electric ana
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walls of the pores. (Positive G ind
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a) b) c) C reso d) δtherm e) p 0 U
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a) b) UA,l c) d) E 0 Q A Q A TA TA
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tor. This eliminates the need to le
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to this consumption of acoustic pow
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The traditional Stirling refrigerat
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Washington 1986) pp. 550-554, Softw
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258 Part B Physical and Nonlinear A
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Acoustics 9. Acoustics in Halls for
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parameters, so we can assist in bui
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weeks or even years is less reliabl
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9.3.1 Reverberation Time Reverberan
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selected). A distance different fro
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ing sound, as will naturally be exp
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of the sound fields. Consequently,
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e derived from interrupted noise de
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Acoustics in Halls for Speech and M
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espectively, can be calculated from
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ated by the architects. However, on
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of C and G. However, as all the ind
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F b d F n I S Fb Fn S d F n/F b d/d
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HS S èn ã d0 P0 rn Position of ey
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Time T (s) 2.5 2 1.5 1 5 10 15 Acou
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floor can be tilted to reduce volum
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ÄLcurv (dB) 10 8 6 4 2 0 -2 -4 -6
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Seating capacity 2662 1 915 + 324 2
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4 3 2 1 Acoustics in Halls for Spee
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cially in auditoria with T values l
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esonance (AR)andmultichannel reverb
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Concert 10. Concert Hall Acoustics
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Concert Hall Acoustics Based on Sub
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0 0 Concert Hall Acoustics Based on
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mately by Concert Hall Acoustics Ba
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10.1.5 Specialization of Cerebral H
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The other (n − 1) bits indicated
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As for the conflicting requirements
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have mainly been concerned with tem
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a) c) S S -4.3 -2.8 -2.0 -3.5 -3dB
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a model of the auditory-brain syste
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Building 11. Building Acou Acoustic
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Pressure Maximum Minimum 0 D Distan
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Table 11.1 Absorption coefficients
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Absorption coefficient α 1 0 Frequ
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is of key importance in rooms where
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Table 11.4 Transmission loss and ST
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TL of wall - (TL of door, window or
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Table 11.7 Generalized noise reduct
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Masking sound pressure level (dB) 5
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As for the room criterion (RC) meth
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11.5 Noise Control Methods for Buil
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Neoprene pads (30 durometer) with a
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Concrete Caulk around perimeter Vib
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Trim board to conceal gap (fasten o
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Gypsum board partition (as schedule
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Double-layer ribbed or waffle neopr
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11.6 Acoustical Privacy in Building
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Table 11.9 AI,SIIandPIforopenplanof
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Electronic sound masking in plenum
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E 1179 Standard Specification for S
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430 Part D Hearing and Signal Proce
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Psychoacoust 13. Psychoacoustics Ps
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Absolute threshold (dB SPL) 100 90
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the signal. By using this off-cente
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is as a crude indicator of the exci
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Relative response (dB) 100 90 80 70
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In a variation of this procedure, t
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Level of matching noise (dB) 100 90
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13.4 Temporal Processing in the Aud
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Most models include an initial stag
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The components were either uniforml
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(Frequency DL)/ERBN 0.2 0.1 0.05 0.
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elaborate place models have been pr
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13.6 Timbre Perception 13.6.1 Time-
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the duplex theory of sound localiza
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harmonic (by shifting the frequency
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sive. While some studies have been
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sentences (see Fig. 13.20). They va
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components is usually only perceive
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References 13.1 ISO 389-7: Acoustic
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13.74 D. Ronken: Monaural detection
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asymmetric function, J. Acoust. Soc
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13.211 J. Vliegen, A.J. Oxenham: Se
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534 Part E Music, Speech, Electroac
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The 16. The Human Human Voice in Sp
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uation, the effect of gravity is in
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piratory muscles (the internal inte
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Mean Ps (cm H2O) 50 40 30 20 10 0 D
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Glottal flow Closed Opening Open Cl
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Transglottal airflow (l/s) 0.4 0.2
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Mean spectrum level (dB) -30 -40 -5
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20 10 0 -10 -20 -30 -40 -50 0 i y u
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Mean level (dB) 0 -10 -20 -30 -40 1
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This topic was addressed by Ladefog
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Fig. 16.29 Acoustic consequences of
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Bass i e u Alto Tenor o ε œ æ Th
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100 80 60 40 20 0 -20 100 80 60 40
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tours for [� ]and[Ù ] sampled at
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Rapp [16.100] asked three native sp
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Utterance command T0 T3 Accent comm
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The # symbol indicates the possibil
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Second formant frequency (Hz) 2500
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tional rather than absolute (à la
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16.7 P. Ladefoged, M.H. Draper, D.
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esonance imaging: Vowels, J. Acoust
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16.139 A. Eriksson: Aspects of Swed
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Computer 17. Computer Mu Music This
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Quantum step Amplitude Quantization
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Some might notice that linear inter
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pers, textbooks, patents, etc. Furt
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0:00.0 0.5 0 Computer Music 17.3 Ad
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(0,0) (0,1) (1,1) (0,2) (1,2) (0,3)
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synthesizing vocoder. The main diff
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x(n) + z -1 z -1 Scattering junctio
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230 Hz FOF 1100 Hz FOF 1700 Hz FOF
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0 y + - Computer Music 17.8 Physica
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-1 (1-ß )×length Velocity + Veloc
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0 -30 (dB) -60 0 1.5 3 4.5 (kHz) Fi
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17.10 Composition The history of co
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and variance of the features can be
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17.20 J.L. Kelly Jr., C.C. Lochbaum
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Audio 18. Audio and Electroacoustic
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Alexander Graham Bell filed his pat
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on magnetic stripes. A common arran
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60 40 20 0 SPL-sound pressure level
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Interaural intensity difference (dB
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with equalization, without incurrin
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Fig. 18.8 Sine wave with crossover
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a) b) c) 100 0 V mV 10 0 a = 13 a =
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Ultrasound contact gel Position enc
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a) 10 cm b) c) 10 cm Fig. 21.32a-c
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a) Pin B Pin A Ultrasound line b) M
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Organ Patient Ultrasound transducer
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systems cannot tell the difference
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40 µm can be resolved. For a 10 kH
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a) b) c) d) Medical Acoustics 21.4
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Fig. 21.54 Doppler spectral wavefor
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10 20 30 10 20 30 Pre-exercise B-mo
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Vibrations in a punctured artery De
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the veins and diffuse into the inte
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21.5.3 Agitated Saline and Patent F
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transported by those cells and/or r
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1 0.8 0.6 0.4 0.2 0 Relative power
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High intensity focused ultrasound h
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a) b) c) Fig. 21.74a-c B-mode imagi
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provided simple metrics for the lik
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thickness of the carotid arteries,
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Structural 22. Structural Acoustics
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Structural Acoustics and Vibrations
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Magnitude (arb. units) 1.4 1.2 1.0
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This does not include the case wher
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the mass matrix is taken to be cons
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Magnitude (dB) -10 -30 -50 0 1 2 3
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where D(ω) = ω 4 − 2iω 3�
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form y(x, t) = � Φn(x)qn(t) . (2
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first to solve the wave equation (2
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5 3 1 -1 -3 -5 0 1 2 3 4 5 6 7 8 9
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conditions at each end) are necessa
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from which we can derive through (2
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In this case, the eigenfrequencies
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of radiation modes and their link w
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Finally, the displacement is ˜ξ(x
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notes the value of this eigenmode a
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Pm = ˙Q H [Rs + Ra] ˙Q , (22.262)
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where and Ra = 2ζaω0 M Z(s) = zL
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Radiated Power. The mean acoustic p
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(22.318) can be written ξ(x, y, t)
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Denoting the eigenfrequencies and e
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Magnitude (arb. units) 3 2 1 0 -1 -
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for any real symmetric tensor Xij.
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F(N) 1 0.5 0 -0.5 -1 -1 -0.8 -0.6 -
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whose solution is θ1 = A cos ωτ.
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4.5 3.5 2.5 1.5 A 0.5 0 0.5 1.0 1.5
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Equations (22.423) are usually writ
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3. As the amplitude reaches the top
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Shallow Spherical Shells and Plates
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22.20 L. Cremer, M. Heckl: Structur
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Noise Noise is discussed in terms o
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where the overbars represent time a
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Typical outdoor setting A-weighted
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90 dB(A)” is widely used, and imp
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Microphone, amplifier and A/D conve
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When each segment of the measuremen
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found from � LW = Lp + 10 log A +
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surement method is the ultimate use
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An intensity analyzer is more compl
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23.2.5 Criteria for Noise Emissions
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Table 23.5 Table of limit values fr
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a) Air flows freely to rotor Weak t
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Static efficiency normalized to its
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ful applications. Good results are
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Table 23.8 Crossover speeds for var
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Reduction of airplane engine noise
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A variety of materials are used to
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∆LF (dB) 0 -10 -20 α -30 0.05 0.
Page 994 and 995:
Absorption coefficient 1.0 0.8 0.6
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high enough that there is little so
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23.4.4 Criteria for Noise Immission
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Table 23.10 (cont.) Some features o
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Noise 23.4 Noise and the Receiver 1
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view of administrative procedures r
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provides recommendations for a foll
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sound power levels of noise sources
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23.68 ISO: ISO 9296:1988 Acoustics
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in impedance tubes - Part 2: Transf
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23.194 Commission of the European C
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1022 Part H Engineering Acoustics P
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Sound 25. Intens Sound Intensity So
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Under such conditions the intensity
Page 1050 and 1051:
a) Pressure and particle velocity 0
Page 1052 and 1053:
τ is a dummy time variable. The ca
Page 1054 and 1055:
Error in intensity (dB) 5 0 -5 -10
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8 7 6 5 4 3 2 1 0 -1 -2 -3 Error du
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crophones are calibrated with a pis
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Sound power level (dB re 1 pW) 72 7
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it is relatively straightforward si
Page 1064 and 1065:
intensity normal to the source. Thi
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25.9 W. Maysenhölder: The reactive
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25.77 ISO: ISO 11205 Acoustics - No
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Optical 27. Optical Methods Metho f
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course also present in ordinary hol
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Optical Methods for Acoustics and V
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50 100 150 200 250 300 350 400 450
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a) b) Optical Methods for Acoustics
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nm 1000 0 -1000 150 y (mm) 100 50 O
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Laser Optical Methods for Acoustics
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References 27.1 E.F.F. Chladni: Die
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27.75 E.-L.Johansson, L. Benckert,
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About the Authors Iskander Akhatov
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Neville H. Fletcher Chapter F.19 Au
Page 1134 and 1135:
Brian C. J. Moore Chapter D.13 Univ
Page 1136 and 1137:
Detailed Contents List of Abbreviat
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3.8.3 Acoustic Power ..............
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4.8.3 Typical Speed of Sound Profil
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7.3 Engines .......................
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10 Concert Hall Acoustics Based on
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13.4 Temporal Processing in the Aud
Page 1148 and 1149:
15.2.5 String-Bridge-Body Coupling
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19.6 Birds ........................
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22.4.5 Combinations of Elementary S
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24.8 Overall View on Microphone Cal
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Subject Index 3 dB bandwidth 463 A
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British Medical Ultrasound Society
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electric circuit analogues - acoust
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hyperspeech 703 hypospeech 703 I IA
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- participation factors 909 - stiff
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- musical instruments 541 - musical
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- nonlinear vibrations 957 - plate
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subjective preference theory 353 su
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Introduction to Acoustics

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