Acoustics for engineers: Troy lectures

Acoustics for Engineers: Troy Lectures

Volumn , Issue , 2008, Pages 1-233

  Blauert, Jens ^a   Xiang, Ning ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

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EID: 84885807855     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-76348-2     Document Type: Book

References (60)

1. The sound-field can, for example, be calculated with the Kirchhoff-Helmholtz integral equation that determines the sound field inside an enclosed space from the sound-pressure and the pressure-gradient distributions on an enclosing surface
2. The Kirchhoff-Helmholtz integral equation then reduces to the so-called Rayleigh or Huygens-Helmholtz integral-see Section 10.1
3. As mentioned before, we prefer the letter symbol β to k.wave number
4. Recall that we had already introduced α with the exponential wave in Section 8.3. There, however, the damping was caused by geometric expansion of the wave and not by dissipation
5. In the analogous circuit of Fig. 11.1, viscosity corresponds to R' and thermal conduction to G'
6. Note that a medium with fully enclosed, that is, mutually unconnected cavities is not porous. Artificial foams can be produced both ways, that is, either with or without connections between the internal voids (gas bubbles)
7. Consult Section 1.6 for incoherent superposition
8. The chunks of sound energy that the source sends out and that subsequently oscillate between the two walls are sometimes dubbed "sound particles"
9. This is the case for rectangular rooms where many mirror sources coincide spatially due to the rectangular corners. In more irregular rooms the situation may become more complicated, particularly, when focussing occurs
10. In order to measure α for perpendicular sound incidence only, a measuring tube may be applied-see Section 7.6
11. With p rms being the rms-value of p-see Section 15.4 for a definition
12. w
13. 0
14. In signal theory the same term is used for stochastic signals that are not prone to carry information
15. It is worth noting that the influence of wind leads to violation of the principal of reciprocity
16. To increase their efficiency, capsules should have some sound-absorbing material inside
17. Barriers in enclosed spaces are only sensible if the ceiling above them is absorbing
18. The sound level may actually increase at the input port of a muffler, due to reflection
19. If one can accept that media flow will be hindered, the duct may be entirely filled with absorbing (porous) material, a condition called a throttling muffler
20. Long-time exposure to noise levels above 85 dB in the mid-frequency range may cause permanent impairment of hearing. These levels are not at all uncommon in daily life, especially in places like discotheques or when using headphones. Levels above 130 dB may affect inner organs and may cause symptoms like vertigo and nausea
21. In contrast to Section 14.4 the term active has a different meaning here. Here it denotes that devices have controlled power sources of their own and an output power that exceeds the input power
22. 3
23. → must not be mistaken as a particle velocity!
24. We present rms-values rather than peak values in the following synopsis to account for all kinds of finite-power sounds, such as noise, speech and music, besides sinusoidal sounds. See Appendix 15.4 for the definition of rms. Peak values of sinusoidal signals-as usually used in complex notations throughout this book-exceed their rms-values by a factor of □2, that is x=□2 x rms
25. Note that deciBel [dB] and Neper [Np] are no units in the strict sense but letter symbols indicating a computational process. When used in equations, their dimension is one
26. In network theory, double-logarithmic graphic representations are know as Bode diagrams
27. Newton's law is valid in so-called inertial spatial coordinate systems. These are such in which a mass to which no force is applied moves with constant velocity along a linear trajectory. As origin of the coordinate system we usually use "ground", which is a mass taken as infinite. Gravitation forces are not considered here
28. In acoustics, the compliance, n, is often preferred to its reciprocal, the stiffness, k=1/n, as this leads to formula notations that engineers are more accustomed to-refer to Chapter 3
29. As noted in the introduction to this chapter, the general exponential function is an eigen-function of linear differential equations. It stays an exponential function when differentiated or integrated
30. We can also deal with cases where the frequency varies slowly, by assuming that a stationary state has (approximately) been reached at each instant of observation
31. a=ε l A with ε being flow resistivity-for details refer to Section 11.5
32. Normally we do not experience the spring characteristics of air because the air can evacuate, but the effect in this case is similar to operating a tire pump with the opening hole pressed closed
33. The names for the analogies are traditional but may make sense in the light of the discussion in Section 3.6
34. An additional type of electroacoustic analogy that allows for waves will be introduced later in Section 8.5
35. In general, higher forces can be achieved with magnetic fields because the electric field-strength is limited by the danger of disruptive discharge. This is the reason that electric motors and generators usually use magnetic fields
36. When using the analogy#1, the transformer would represent the electric-field transducer and the gyrator the magnetic-field tranducer
37. Note that in hearing-aid technology the sound emitter is called receiver because it receives electrical signals
38. Emitters are sometimes also called transmitters, to denote that an electrical signals is transmitted to the sound field
39. δ, the directional characteristic, is the ratio of the magnitude of the driving force taken for a sound incidence from a certain direction compared to the magnitude of the driving force in the direction of maximum sensitivity
40. The name for this kind of transducer, magnetodynamic or just dynamic, is of historic origin. In the terminology of mechanics, transducers of all kinds are dynamic devices
41. For piezoelectric tweeters see Section 6.4.
42. It is possible to derive d from e with the modulus of elasticity, Young's modulus, being known and linearity according to Hook's law being assumed
43. When plotting such curves, it is often advantageous to start with the lossless case and then introduce small losses later
44. Readers who have not yet heard of electromagnetic waves may wish to read Sections 7.1-7.2 first
45. These quantities are taken from thermodynamics, where cp is the specific heat capacity at constant pressure and cv the specific heat capacity at constant volume
46. The characteristic field impedance, Zw, also known as wave impedance, will be introduced in Section 7.4
47. We must check whether this linearization is still justified when the medium is flowing fast as it would in an exhaust system, and/or if we have rapid changes of v over x as would occur at area steps in a tube. It is worth noting that the second term is the more significant one in flow dynamics while the first term is typically neglected there
48. This form can also be derived by combining the differential of (7.19) by x with that of (7.26) by t
49. In physics this quantity is often called wave number or, more precisely, angular wave number and denoted by k. In fact, it is not a "number" since is has the dimension [1/length]
50. γ is called complex propagation coefficient, also denoted complex wave number k. We shall make use of it later, particularly, in Sections 8.3 and 11.2
51. w becomes necessarily complex with the addition of an imaginary component
52. This name originates from electrical engineering where the same equations hold but with p being replaced by u and v by i
53. In the literature, these terms are often called reflection coefficient and absorption coefficient. However, their dimension is [1] and their value range is 0-1, or 0%-100%, respectively. This is why we prefer the term degree
54. The theory of Kundt's tube is homomorphic to the theory of the measuring line for electromagnetic waves. To convert reflectances into impedances, and vice versa, a graphical tool called Smith chart is useful. It converts an image of the complex Z-plane onto an image of the complex r-plane
55. 1, have positive values
56. Webster's equation for v looks different from that as derived above for p
57. This, by the way, contributes to the characteristic sound of horn loudspeakers
58. Spherical harmonics are eigen-functions of the wave equation in spherical coordinates
59. Please note that loudspeakers in closed cabinets become spherical radiators at low frequencies-refer to Section 9.5. Their low-frequency-response can thus be optimized by appropriate placement
60. An application of this algorithm, based on the directional equivalence of emitters and receivers-see next Section-is the electronic steering of SONAR antennas