ERRATA AND ADDITIONS FOR "ENGINEERING NOISE CONTROL" 4th Edn. First printing April 3, 08 p4, Eq..3 should not have the ± symbol on the RHS p36, 3 lines from the bottom of the page, replace cos b with cos β p68, In Equation (.4), change K to C, where C is the viscous damping constant and define κ as the segment stiffness p8, 7 lines below heading 3.3.., change 008" to 005". p0, In Equation (3.9), remove the! sign following the = sign p, In Eq. (3.35), P P should be p 0 p 0 and I n should be I p, 5 lines above Eq. 3.37, change " Jacobsen, 008" to " Jacobsen and de Bree, 005" p67, 80, replace AS07-987" with AS07-000" p95, Equation (5.33) should be: Q 0 ' 4πa A a % jka a e &jka ' 4πA( % jka)e &jka (5.33a,b) p96, Equation (5.36) should be: p(r, θ, t) ' jkρcq 0 ( % jka) [&G(r, h, ω) % G(r j(ωt % ka), &h, ω)] e ' jkρcq 0 ( % jka) (5.36a,b) j(ωt % ka) &G(r & hcosθ, h, ω) % G(r % hcosθ, &h, ω) e p96 In Equations (5.37) and (5.38a), remove the minus sign that follows the equals sign p97 In Equations (5.4), (5.43) and (5.44), remove the minus sign that follows the equals sign p8, In Eq. 5.53, replace k with k p8, In Eq. 5.53, replace (-j) with (+j) p9, In Eq. 5.55, replace (-j) with (+j) p9, Replace Equation (5.57) and the two lines preceding it with:
where g(w) is the scaled complementary error function, erfc( ) is the complementary error function (Abramowitz and Stegun, 965), and w, which is given by Equation (5.53), is a complex number. The calculation of g(w) is a complicated process and the equations to follow can only be used in isolation if the real part of w is less than 0 and the imaginary part is greater than 0 (that is, w is in the second quadrant of the complex plane). So any calculation begins with adjusting the value of w to w a so that the real part is less than 0 and the imaginary part is greater than 0. As w a is complex, we can write,w a = w r + jw i = Re{w a } + j Im{w a }. The calculation of g(w a ) is then undertaken using Equations (5.56) to (5.59). If the original value of w did not need be adjusted to put w in the second quadrant of the complex plane, then g(w) = g(w a ). If the original value of w before adjustment, was such that w was not in the second quadrant of the complex plane, then g(w a ) must be adjusted to obtain g(w), according to the following rules, with rule applied first and rule 3 applied to the result after the application of rules and.. If the imaginary part of w is less than 0, then g(w a ) is replaced with g(w) = exp(-w a ) - g(w a ), where g(w a ) is calculated using Equations (5.56) to (5.59);. If the imaginary part of w is greater than or equal to 0, then g(w) = g(w a ); 3. If the product of the imaginary and real parts of w is greater than 0, then the sign of the imaginary part of g(w a ) is changed (i.e., the complex conjugate of the g(w) that was obtained using the preceding two rules is then the final g(w)). For small w r and w i, where w r is less than or equal to 3.9 and w i is less than or equal to 3: g(w a ) ' g(w r, jw i ) ' K (w i, w r ) % jk (w i, w r ) (5.57a) where, K (w i, w r ) ' hw i w % i h 4 π(w r %w i ) π j %P if w i <π/h %0.5P if w i ' π/h %0 if w i >π/h n' e &n h (w r %w i %n h ) (w i &w r %n h ) %4w r w i & w i π E(h) (5.57b) hw K (w i, w r ) ' r % π(w r %w i ) &F &0.5F w r h π j 4 n' if w i <π/h if w i ' π/h &0 if w i >π/h e &n h (w r %w i %n h ) (w i &w r %n h ) %4w r w i % w r π E(h) (5.57c)
P ' F ' (A C & B D ) exp[w r % (w i π/h) & w i ] (C % D ) (5.57d) (A D % B C ) exp[w r % (w i π/h) & w i ] (C % D ) (5.57e) A 'cos(w r w i ) B 'sin(w r w i ) C 'e &w i π/h &cos(w r π/h) D 'sin(w r π/h) (5.57f) The error bound can be estimated from: E(h)# πe&(π /h ) &e &(π /h ) (5.57g) Note that h is a constant selected by the user. If h=, then E(h)# 0-4 and only 3 or 4 terms are needed in the infinite sums included in the expressions for K and K. If h is reduced to 0.8, then E(h)#0-6 and 5 terms will be needed in the infinite sums included in the expressions for K and K. If h is reduced to 0.5, then E(h)#0-5 and 4 terms will be needed in the infinite sums included in the expressions for K and K. It is recommended that h = 0.8 be used. p9, In Equations (5.58) and (5.59), replace -jw with +jw a and replace w with w a. p9, and lines above Equation (5.58), replace 3 with 3.9 and with 3. p30, In Eq. 5.66, replace k with k p30, In Eq. 5.66, replace (-j) with (+j) p3, Replace the paragraph beginning with The effect of turbulence (including Equation (5.67) and the 3 lines following it) with the following: The effect of atmospheric turbulence on sound over an acoustically smooth surface has been investigated by Clifford (983) and by Raspet (995). The presence or absence of turbulence may be included by a generalisation of their results to give the following general expression for the mean square sound pressure at a receiver located at a direct distance, r, from the source for a spherically symmetric sound source having unit far field sound pressure at m: p t ' R s R s r % (r %r ) % r(r %r ) Tcos[α s & k(r % r & r)] (Pa ) 3
where: α s ' tan Im{R & s } Re{R s } and where the sign of k has been changed here to reflect that positive time dependence is used in this book, whereas negative time dependence has been used by Clifford (983) and by Raspet (995). p47, Replace Equation (5.95) with: A g '&0log 0 % r r %r R s % r r % r R s Tcos α s & k(r %r & r) (db) p48, 4 lines under Equation (5.97), Z s should be Z m p50, line above Eq. 5.0, change (5.98) to (5.00) p55, Table 5.9, column, change the heading from slight to strong and change the bottom entry from D to C. p55, Table 5.9, column 4, change the heading from strong to slight p55, Table 5.9, Footnote a, change close to ground to 0 m above the ground p58, 4 lines above Eq. 5.06, change added to subtracted p74-6, the standards ISO 3743/, ISO 3747 and ISO 374 are not listed at the end of the book. The references are: ISO 374:00, Acoustics - Determination of sound power levels and sound energy levels of noise sources using sound pressure - Precision methods for reverberation test rooms. ISO 3743-:00, Acoustics - Determination of sound power levels and sound energy levels of noise sources using sound pressure - Engineering methods for small movable sources in reverberant fields - Part : Comparison method for a hard-walled test room. ISO 3743-:994, Acoustics - Determination of sound power levels of noise sources using sound pressure - Engineering methods for small, movable sources in reverberant fields - Part : Methods for special reverberation test rooms. ISO 3747:00, Acoustics - Determination of sound power levels and sound energy levels of noise sources using sound pressure - Engineering/survey methods for use in situ in a reverberant environment. p93, Equation (7.6), k should be k z 4
p358, Equation (8.) should be B ' Eh 3 ( & ν ) p364, fig 8.5, the horizontal part of the IIC 50 curve should extend down to 00 Hz p364, 7 lines from the top of the page add curvature of immediately before 500" p365, Equation (8.), change the "+" sign to a "-" sign p365, delete sentence beginning 4 lines above Eq. (8.) and replace with Both IIC and ISO specify a /3 octave band frequency range from 00 Hz to 350 Hz inclusive. p367, In Equation (8.4), the last term in brackets should be multiplied by p37, In Figure 8.8 caption change (= mh) to (= m /h) p374, Equation 8.49 should be replaced with: TL max ' 0log 0 mc L 4ρch % 0log 0 η % 7 (8.49a,b) ' 0log 0 mc L h % 0log 0 η & 47.4 db (at 0EC) p374, Replace Lgunggren (99) with Ljunggren (99) p378, line, replace 8.39" with 8.38" p397, The second term in brackets in Eq (8.76) is missing a minus sign - it should be 0 &TL/0 p404, Line 3 of item in the solution, change 7." to 33.7" p43, 3 lines below Eq. (8.03), the reference to Eq (8.00) should be Eq. (8.0) p4, Item 3, N = (/R)(.5) should be N = (/λ)(.5) p4, Add the following to the end of item 3, As there are 3 diffracted paths around the building for sound arriving at the rear wall, the power level on the rear wall should be increased by 0log 0 (3)=4.8 db, so the total power on the rear wall becomes 7.8 db. p4, Two lines from the bottom, change 67 to 7.8 and change 79 to 80. p43, Line, change 80 to 8 5
p43, first equation, change 80 to 8 and change 74 to 75 p43, Figure 8. is missing - see below. 50 40 Octave band insertion loss 30 0 0 0 63 5 50 500 000 000 4000 8000 Octave band centre frequency (Hz) Figure 8. Typical pipe lagging insertion loss for 50 mm glass fibre, density 70-90 kg m -3, covered with a lead/aluminum jacket of 6 kg m - surface density. The I symbols represent variations in measured values for three pipe diameters (75 mm, 50 mm and 360 mm). p443, In Eq. (9.5), replace ( - M ) with ( - M ) p449, Following Eq. (9.46), add In the presence of a mean flow of Mach number, M, in the duct, the RHS of Equations (9.45), (9.46) and (9.47) should be multiplied by ( - M). p449, Replace Equation (9.44) with the following equation, where S V is the cross sectional area of the volume. ω 0 ' c & 3R e S V % R V S R 3 e S V % 3R e S V % R V S R 3 e S V % 3S R 3 e S V R V p454, Last term in Equation (9.65), replace A T with (A T /Z s ) 6
p456, After Eq. (9.75), add, Note that in the presence of grazing flow of Mach number, M, Equations (9.69) to (9.75) can be used by substituting ( - M )R e for R e in all places. p467, 3rd line above Eq. (9.0), Change "Figure 9.a" to "Figure 9.a". p47, nd and 5 th lines from the top, change undamping to nonlinear p473, In Eq. (9.4), the right hand side should be multiplied by the gas density. p477, Top label in Figure 9.4, change quadruple to quadrupole. p478, Line 8 under heading 9.8, change undamping to non-linear. p48, line, change height to width. p487, Figure 9.0 legend should be curve no 3 4 σ ρh 0.0 0. 0.5 p488, Figure 9. legend should be curve no 3 4 σ ρh 0.0 0. 0.5 p490, bottom line, h/r should be h/λ p493, 4 and 9 lines from the bottom, h/r should be h/λ p494, Figure 9.3 caption should have the following sentence added. Note that for a silencer with multiple baffles, S is the cross-sectional area of one airway, not the total silencer. p497, lines from the bottom of the page, change doubled to double p498, 4 th line under Section 9., change 9.5" to 9.6" p499, To avoid confusion with the discussion on p50 (line ), change f 0 to f 0s in three locations above Eq. (9.45) 7
p506, replace second sentence under the heading, 9.5 DIRECTIVITY OF EXHAUST DUCTS with To get the rectangular section data to collapse on to the ka axis for circular ducts, where a is the duct diameter, it was necessary to multiply the rectangular duct dimension (d) in the direction of the observer by 4/π to get a. p508, Figure 9.30 should be 0 θ = 0E Directivity Index (db) 0 0-0 -0 5E 30E 45E 60E 75E 90E 0E E E 50-80 -30-40 0..0 0 00 Exhaust stack directivity index measured in the field vs ka where a is the stack radius. Curves fitted to data reported by Day and Bennett (008). ka p509, first line, change π to π p50, Equation (5.70) should be: w(φ) ' sin(ks d sin(φ)) ks d sin(φ) ( & α st ) (L/d)tan*φ* p59, The spring helix angle, α, can be included in Eq. 0. to give a more accurate result as follows (E is the modulus of elasticity): k ' d 4 cosα 8n C D 3 cos α G % sin α E & p58, 5 lines above Equation (0.36), change Equation (0.0) to Equation (0.) p53, Equation (0.45) should be: M f ' j(k f /ω & ωm f ) & p536, 6 lines under the figure, change undamping to nonlinear 8
p539, Equation (0.53) has a square missing on the second term in the numerator. The correct equation is: *y * ζ Ωm m % Ω & k m k m *F* ' k ζ Ωm m Ω &% m Ω m % k k Ω & Ω & Ω & k m k m However, this equation is only valid for zero damping on the main mass, although it gives quite accurate results provided the damping is relatively small. The equation that includes damping on the main mass is Equation (0.4) in the third edition with the "d " removed from the denominator on the RHS. So if damping, ζ, is included on the main mass, the above equation becomes: *y * ' *F* k & Ω & r/q % ζ Ω % s/q &/ and *y * ' *y * (a/q) % (b/q) / where, Ω ' ω m /k, θ and θ are phase angles of the motion of the masses relative to the excitation force, *F* is the amplitude of the excitation force and: a ' (k /k ) % 4ζ Ω & (m /m )(k /k )Ω b '&ζ (m /m )Ω 3 k q ' & m Ω % 4ζ k m Ω r ' (m /m )(k /k ) Ω & (m /m ) (k /k )Ω 4 % 4ζ (m /m )Ω4 s ' ζ (m /m ) Ω 5 p54, line, change Equation (0.57) to Equation (0.6) p57, Figure.3 caption, although Heitner did use a similar figure to this, it was based on the earlier work published by Ingard so the correct reference should be Ingard, 959". p585, Line following Equation (.55), replace A-weighted internal level with unweighted internal level. p586, Line following Equation (.59), replace A-weighted internal level with unweighted internal level. p643, In Equation (.36), change ψ to n 9
p644, In Equation (.40), change n to ψ p644, In Equation (.40) and in the text in 3 places following the equation, change (x b, y b ) to (x b, y b, z b ) p644, lines below Equation (.40), change n to ψ p65, Third line of footnote, ρ should be ρ m p65, Last line of footnote, in the equation for k B, ω should be replaced with ω p654, In Equation (.6), m p should be M p p654, st line under.3., change equations to equation p657, In step 6, the equation reference should be.6 p657, In the example table, the column header σ (db) should be 0 log 0 σ (db) p660, Eq. A.9 should be F '&LP tot V ' ρ tot V du tot dt (A.9a,b) p669, 4 lines above Eq. C, change undamping to nonlinear p669, Equation C. could be written in a less ambiguous way as R ' ρδpa/( 0mR) ' ΔPA/(V 0 R) p673, Two lines above Eq. C.9 (and and 3 lines from the top of the page), replace complex density with complex density (normalised with respect to the density of of the gas in the porous material). p673, One and two lines above Eq. C.9 (and 3 lines from the top of the page), replace complex compressibility with complex compressibility (normalised with respect to the compressibility of the gas in the porous material). p684, Line under Eq. (C.50), add after cavity the following:, the impedance, Z L for a wave incident at angle, θ, is p684, Line above Eq. (C.5), change C.38 to C.49 p686 3 lines under Equation (C.55), change 9. to 9.5 p75, Remove the 009 reference for Jacobsen and de Bree 0