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. Us*e*

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** = *ρ*_{0}*c*_{0}

Next paragraph – **z** = *az*_{0}

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*