This errata page is a collection of all bugs and mistakes that I noticed for the first edition. If you would like to propose some corrections please send a note to author@alexanderpeiffer.de.
A special thank you goes to Valentin who found all the bugs in chapter 7 and the legend bug in figure 8.38.
Chapter 1
Page 9 – Equation (1.37) – In the paragraph before I say signal , thus the equations should be with
Page 13 – Equation above equation (1.56) – the first integral should read
\Delta E_{\rm cylcle} = \int_0^Tc_v\ddot{u}\,dt=\ldots
Page 15 – Figure 1.11 – left spring should have stiffness
Page 16 – Line below Equation (1.77) – The second frequency should read
Page 31 – Equation (1.147) – The last fraction should read
Page 33
Equation (1.162) – It should be
The last equation must be similar to equation (1.164), thus should be in boldsymbol
Page 34 – Equation (1.167), should also be in boldsymbol
Page 38 – Figure 1.24 – To be consistent with the text it should be and
Chapter 2
Page 44 – Last enumeration – Item 3 should be “The momentum flow out of the volume”
Page 47 – Equation (2.25) – The velocity potential should be
Page 48 – Equation (2.29) – and consequently …
Page 53
Table 2.2 – The acoustic velocity formula should read
Equation (2.59) – The last expression should be
Page 54
Equation (2.65) – It should read
The equation reference (2.30) is not correct it should be (2.65)
Page 55
Equation (2.68) –
Equation (2.69) –
Page 57
Equation (2.85) – It should by instead of
Equation (2.86) – The time average must be used instead of
Page 58 – Equations (2.87) and (2.88) – Same correction as for equation (2.86)
Page 62 – Equations (2.116) and (2.117) – The impedance symbols should be boldmath
Page 58 – Equation (2.98) – This should read
Page 70 – Above equation (2.155) – It should read .
Page 115 – Equation (3.230) – The second term should read
Chapter 3
Page 80 – Equation (3.22) –
Page 111 – Paragraph below (3.21b) – Insert as first sentence: Considering as the real and positive solution, hence .
Page 113 – Equations (3.222)-(3.224) – Replace by
Page 114 – Equation (3.225) – Replace by
Page 115 – Equation (3.231) – In the nominator it should read
Chapter 4
Page 120 Figure 4.1 – The radius is and not
Page 135
Figure 4.12 – Missing unit at y-axis label. Use
Equation (4.76) – It would be more consistent to use as index in the sum
\bm{p}(\vec{r}) = \sum_{m=0}^\infty \bm{p}'_m \Phi_m(\bf{r})
Equation (4.77) – The first integral should read as follows
\int_{V} \sum_m^\infty\bm{p}_m'\Phi_m(\bf{r}) (\bm{k}^2 - k_n^2) \Phi_n(\bf{r}) dV
Equation (4.78) – There must be a in the sum over .
Page 136 Equation (4.84) – Remove conjugate star, not required for real modes
Page 137
Paragraph below Equation (4.86) – it should read
Equation (4.87) – Third term must be
Page 141 Last paragraph – first element and not fist element
Page 141 Equation (4.103) – For better consistence with Figure 4.16 would be better
Chapter 5
Page 151 Section 5.3.1 – First sentence – it should be in-homogenous form.
Chapter 6
Page 161 Equation (6.3) – The square should be removed and it should read
Page 166
In the first line the formula should read
Equation 6.21 – The in the first line should be removed
Page 169
Equations (6.33)-(6.35) – The factor is missing for all sums.
Equations (6.34)-(6.35) – The last should read
Page 170
Equations (6.37) – Remove the hat from all pressure symbols is correct
Equations (6.38) – Replace by
Page 175/176 Figure 6.9 and 6.10 – Right hand side. Label of y-axis: should not be boldsymbol
Page 180
Equation (6.63) – The nominator should read
Equation in section 6.4.1.4 – should not be boldsymbol. However, for figures 6.17 and 6.18 I used equation (3.225)
Section 6.4.2 – It is worth mentioning that the plate is made of aluminum
Figure 6.14 – The density variation in the caption should be 2% not 1%
Page 192 – Equation below (6.92) – Second sine should include a and not an
Chapter 7
Page 207 Equation (7.18) – The last radiation stiffness should be instead of
Page 208
Section 7.3.1 heading – Exchange m and n
Globally it would be better to stay with the original heading and exchange and in the text and all formulas, because his would correspond better to figure 7.5
Equation (7.22) – The index is missing, it should be
Page 210 Equations (7.28) and (7.30) – The index should be used consequently in all formulas as sum index
Page 211 Equation (7.32) – The factor is missing after both large parenthesis
Page 215
Equation (7.40) – instead of
Last line of last paragraph – response instead of reponse
Page 218 Figure 7.13 – The SEA-Matrix must read instead of
Page 220 Equation (7.47) – The modal coordinate is missing
Chapter 8
Page 226 Last paragraph – … is modified by an factor instead of
Page 227 First sentence – must be replaced by
Page 231 Figure 8.5 – Label of y-axis: TL/dB instead of TL in dB Page
Page 233 Figure 8.8 – Due to a bug in the code spring curves are wrong. See new figure.
Page 234 Figure 8.10 – Label of y-axis: TL/dB instead of TL in dB
Page 238 This item in description – instead of
Page 242 Equation (8.74) – The equal sign before the must be removed
Page 239 Equation (8.51) – in the first row the integral is missing, The second integral runs over
\Pi = \frac{1}{2} \int_S Re\{ {\bm v}_z^*(x,y){\bm p}(x,y) \} dS
Page 240 Equation (8.59) – last sine should read
Page 245 Equation (8.73) – The stiffness is complex, thus
Page 247 Equation (8.94) – The stiffness is complex, thus and there is an missing in the last term
\bm{D}_{\rm tot}''(k_a,\vartheta)=m''\omega^2\left[\frac{ k_a^4\sin^4\vartheta}{k_B^4} -1 \right] - j\omega\frac{2 \rho_0c_0}{\cos\vartheta}
Page 250
Equation (8.101) – it should read
Equation (8.103) – remove useless in the middle
Page 251 Equation (8.105) – use and
Page 253 After Equations (8.108a-d) – it should read
Page 255 Coordinate vector after Equation (8.118) – use bold
Page 256
Equation (8.21) – the displacement vector is missing after the first matrix
Equation (8.23) – the amplitude vector is missing after the second matrix
Equation (8.24) – the displacement vector is missing after the first matrix and
Page 258 Equation (8.131) – is should read
Page 261
Equation (8.143) – wrong index index in excitation cspd. It should be
Equation (8.147) – wrong index index in center matrix cspd. It should be
Page 263
Figure 8.30 – wavenumber vector labels and must be exchanged
Equation (8.151) – is should read
Page 267 Figure 8.38 – The legends must be exchanged. The blue line belongs to
Chapter 9
Page 287
Equation (9.76) – – Should be
Paragraph before Equation (9.78) – Should be small
Page 299
Equation (9.107d) – Division by porosity is missing. Use in nominator
Equation (9.107e) – Variables should be in boldsymbol. Use
Equation (9.107f) – Variables should be in boldsymbol. Use
Equation (9.107g) – Variables should be in boldsymbol. Use
Page 301
Equation (9.109) – The last term of the denominator should read
Equation (9.110) –
{\bm R}(\vartheta)=\frac{{\bm z}(\vartheta)-\frac{{\bm z}_s(\vartheta)}{\cos(\vartheta)}}{{\bm z}(\vartheta)+\frac{{\bm z}_s(\vartheta)}{\cos(\vartheta)}}
Page 302
Paragraph below Equation (6.72) – z = ρ0c0
Next paragraph – z = az0
Page 309 Figure 9.40 – Label of y-axis: First ‘perf’ index should be in roman
Page 313 Figure 9.44 – Figure caption has an index error. It should read
Page 314 Figure 9.45 – Figure caption has an index error. It should read
Page 316 Figure 9.47 – Wrong figure. Should be as follows:
Chapter 10
Section 10.2.1
I really apologize for all the bugs in this section. This is an excellent example that some mistakes of a derivation are not found, because the final result was know before. In fact all equations of this section are wrong, except the final result!
Page 321
In equation (10.3) the diagonal must be corrected
\omega\begin{bmatrix} n_1(\eta_{11} + \eta_{12}) & -n_2 \eta_{21}\\ -n_1 \eta_{12} & n_2 (\eta_{22} + \eta_{21}) \end{bmatrix} \begin{Bmatrix} E_1/n_1(\omega) \\ E_2/n_2(\omega) \end{Bmatrix} = \begin{Bmatrix} \Pi_1 \\ \Pi_2 \end{Bmatrix}
Page 322
This has consequences on equation (10.4)
\begin{Bmatrix} E_1/n_1 \\ E_2/n_2 \end{Bmatrix} = -\frac{1}{\omega^2( \eta^2_{12} n_1 - n_2 (\eta_{11}+\eta_{12})(\eta_{22}+\eta_{21})) } \begin{bmatrix} \frac{n_2}{n_1}\eta_{22} + \eta_{12} & \eta_{12}\\ \eta_{12} & \eta_{11} + \eta_{12} \end{bmatrix} \begin{Bmatrix} \Pi_1 \\ \Pi_2 \end{Bmatrix}
and on (10.5)
E_1 = - \frac{n_1\eta_{12} +n_2\eta_{22}}{\omega^2(n_1\eta^2_{12} - n_2(\eta_{11}+\eta_{12})(\eta_{22}+\eta_{21})}\Pi_1
and (10.6)
E_2 = - \frac{n_2\eta_{12} }{\omega^2(n_1\eta^2_{12} - n_2 (\eta_{11}+\eta_{12})(\eta_{22}+\eta_{21})}\Pi_1
Not to speak about (10.7) and (10.8)
p_{1,\rm rms} = -\frac{\rho_0}{2\pi^2c_0 n_1} \frac{n_1\eta_{12} +n_2\eta_{22}}{n_1\eta^2_{12} - n_2 (\eta_{11}+\eta_{12})(\eta_{22}+\eta_{21})}\Pi_1
p_{2,\rm rms} = -\frac{\rho_0}{2\pi^2c_0} \frac{\eta_{12} }{n_1\eta^2_{12} - n_2 (\eta_{11}+\eta_{12})(\eta_{22}+\eta_{21})}\Pi_1
The pressure ratio (10.9) also has totally different look
\frac{p^2_{2,\rm rms}}{p^2_{1,\rm rms}} = \frac{n_1(\omega)\eta_{12}}{n_1(\omega)\eta_{12}+n_2(\omega)\eta_{22})}
Leaving different result for the coupling loss factor in equation (10.10). Note the involved ratio of modal densities.
\eta_{12} = \frac{p^2_{2,\rm rms}}{p^2_{1,\rm rms}}\frac{n_2(\omega)}{n_1(\omega)\left(1-\frac{p^2_{2,\rm rms}}{p^2_{1,\rm rms}}\right)} \approx \eta_{22}\frac{p^2_{2,\rm rms}}{p^2_{1,\rm rms}}\frac{n_2(\omega)}{n_1(\omega)}
To be precise, the volume in equation (10.11) is
\eta_{22} = \frac{A_s c_0}{4 V_2 \omega}
Page 323
The volume in the – relationship must be and this – in combination with the modal density ratios – gives the final result in equation (10.12).
\left<\tau_{12}\right> = \frac{4 V_1 \omega}{c_0 S_j} \eta_{12} = \frac{p^2_{2,\rm rms}}{p^2_{1,\rm rms}}\frac{V_1 n_2(\omega)}{V_2 n_1(\omega)} \frac{A_s}{S_j} = \frac{p^2_{2,\rm rms}}{p^2_{1,\rm rms}}\frac{A_s}{S_j}
Page 325 Figure 10.4 – Label at y-axis should be
Page 327
Figure 10.7 and 10.8 are not correct due to a bug in the pyva software
Page 328 Figure 10.9 is not correct due to a bug in the pyva software
Chapter 12
Page 361 Figure 12.1 – The Helmholtz number should be
Page 372 – Section 12.3 Last sentence of first paragraph – prototype instead of pototype.
Appendix A
Page 424 Equations (A.68),(A.70)-(A.73) – The force symbol should be in capital letters
Appendix B
Page 426 Equation (B.17) – The upper index should read
Page 429 Figure B.2 – wavenumber vector labels and must be exchanged
Page 436 Equations (B.79-80) – The upper right coefficient in the matrix requires a second right parenthesis
Index
Page 445 coupling loss factor, non-resonant and resonant instead of resonsant