Appendix E: Nomenclature

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a acceleration, m/s2 or ft/sec2

dimension of a panel, m or ft, Eq. (4-152)

number of absorption units, m2 or ft2, Eq. (7-30)

tube diameter, m or ft, Eq. (8-5)

ab barrier coefficient, Eq. (7-90)

amax maximum vibratory acceleration, m/s2 or in/sec2

ar sound power reflection coefficient, Eq. (4-91)

at sound power transmission coefficient, Eq. (4-88)

A constant of integration, Eq. (4-38)

cross-sectional area, m2 or ft2, Example 4-9

constant in Eq. (5-57)

distance for barrier calculation, m or ft, Eq. (7-89)

function defined by Eq. (9-140)

A_ conversion function, dB, Eq. (3-7)

b dimension of a panel, m or ft, Eq. (4-152)

B isothermal bulk modulus, Pa or lbf=ft2, Eq. (2-2)

constant of integration, Eq. (4-38)

flexural rigidity, N-m or lbf -ft

constant in Eq. (5-57)

distance for barrier calculation, m or ft, Eq. (7-89)

function defined by Eq. (9-141)

BT blade tone component of fan noise, dB, Table 5-1

c speed of sound, m/s or ft/sec

cL speed of longitudinal sound waves, m/s or ft/sec, Eq.

(4-156)

Copyright © 2003 Marcel Dekker, Inc.

cp specificheatat constant pressure, J/kg-KorBtu/lbm-8R

cv specific heat at constant volume, J/kg-Kor Btu/lbm-8R

C1 ј Cg=CV coefficient ratio

CA acoustic compliance, m3=Pa or ft5/lbf

CD dissipation coefficient, Pa-s

grille pressure drop function, Eq. (5-70)

CE electrical capacitance, F

Cg valve-sizing coefficient for gas flow, Eq. (5-43)

Ck coefficient in Eq. (9-148)

Cm regression constant in Eq. (8-181)

CM ј 1=KS mechanical compliance, m/N or in/lbf

CS specific mechanical compliance, m3/N or ft3=lbf, Eq.

(4-138)

CV valve-sizing coefficient for liquids

Cw volume compliance of a panel, m5/N or m3/Pa

CF correction factor for composite noise rating, dB, Eq.

(6-6)

CF1;CF2; . . . ;CF7 factors to convert to octave band sound pressure

levels, dB

CFDN correction factor for day–night level, dBA, Eq. (6-

9)

CFg factor to convert to octave band sound pressure levels

for a grille, dB

CFA A-weighting conversion factors, Table 2-4

CFC C-weighting conversion factors, Table 2-4

d spacing between panels, m or ft, Eq. (4-175)

center-to-center spacing of ribs, m or ft, Eq. (4-186)

inside diameter of a vent tube, m or ft, Eq. (5-38)

mean free path for sound in a room, m or ft, Eq. (7-

23)

slant distance in a plenum chamber, m or ft, Eq. (8-

185)

static deflection, m or ft, Eq. (9-16)

dw spring wire diameter, m or in

D acoustic energy density, J/m3

diameter of a cylinder, m or ft

mean diameter of a spring, m or in

DD acoustic energy density for the direct field, J/m3, Eq.

(7-3)

De equivalent diameter, m or ft

DE equivalent distance for traffice noise, m or ft,

Eq. (5-74)

Nomenclature 515

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DR acoustic energy density for the reverberant field,

J/m3, Eq. (7-4)

Dt tower diameter, m or ft

DI directivity index, dB, Eq. (2-28)

_e voltage drop, V

E energy, J

f frequency, Hz

fb blade pass frequency for compressor, Hz, Eq. (5-20)

fB blade pass frequency for a fan, Hz, Eq. (5-12)

fc critical or wave coincidence frequency, Hz

fn undamped natural frequency, Hz

fo octave band center frequency, Hz

peak frequency for a gas jet, Hz, Eq. (5-40)

resonant frequency for a Helmholtz resonator, Hz

_fP width of the TL plateau, Hz, Table 4-1

F force, N or lbf

pressure function, Eq. (5-57)

temperature function, Eq. (4-229)

F1; F2 quantities defined by Eqs (8-142) and (8-143)

Fd damper force, N or lbf

Fs noise spectrum function, dB, Eq. (5-64)

FS spring force, N or lbf

Fsb side-branch noise spectrum function, dB, Eq. (5-66)

FT transmitted force, N or lbf

g local acceleration due to gravity, m/s2 or ft/sec2

gc units conversion factor, 1 kg-m/N-s2 or 32.174 lbm-ft/

lbf -sec2

G shear modulus, Pa or lbf /ft2

G1;G2 quantities defined by Eqs (8-146) and (8-147)

h thickness of a panel, m or ft

fraction of molecules that are H2O, Eq. (4-227)

distance water falls in a tower, m or ft, Eq. (5-32)

ho distance between the bottom of packing and pond

surface, m or ft, Eq. (5-32)

hp depth of packing below tower ring beam, m or ft, Eq.

(5-32)

hr height of ribs on a panel, m or ft, Eq. (4-186)

H dimension of plenum chamber, m or ft, Eq. (8-185)

Hр_; ’Ю pressure distribution function, Eq. (2-29)

Ho free height of a spring, m or in

Hs solid height of a spring, m or in

i electric current, A

516 Appendix E

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I acoustic intensity, W/m2

area moment of inertia, m4 or ft4, Eq. (4-189)

IL insertion loss, dB, Eq. (7-76)

Im imaginary part of a complex number, Eq. (4-21)

j ј

ffiffiffiffiffiffiffi

p_1 imaginary number

k wavenumber, m_1 or ft_1

kt thermal conductivity, W/m-K or Btu/hr-ft-8F

Kf greatest common factor, Eq. (5-20)

KL pressure function, Eq. (5-51)

Ko constant, dB, Eq. (5-18)

KS quantity defined by Eq. (4-143)

spring constant, N/m or lbf /in

L quantity defined by Eq. (4-95), m or ft

thickness of a wall, m or ft, Eq. (4-115)

dimension used in predicting NEF contours, Sec.

6.9

tube length, m or ft, Eq. (8-6)

expansion chamber muffler length, m or ft

Lo A-weighted sound level for stationary locomotive,

dBA, Eq. (5-82)

L1 A-weighted sound level for train passby, dBA, Eq. (5-

84)

L10; L50; L90 A-weighted sound levels that are exceeded 10%,

50%, or 90% of the time, respectively

La vibratory acceleration level, dB

LA A-weighted sound level, dBA

LCNR corrected composite noise rating, dB, Eq. (6-6)

Ld displacement level, dB

LD acoustic energy density level, dB

energy-equivalent pressure level during the daytime,

dBA, Eq. (6-8

LDN day–night sound level, dBA (DN)

Le equivalent length, m or ft, Eq. (8-12)

LE mutual inductance, H

LEPN effective perceived noise level, dB(PN), Eq. (6-14)

Leq energy-equivalent sound level, dBA, Eq. (6-7)

LF vibratory force level, dB

LG sound pressure level gain for a resonator, dB, Eq. (8-

62)

LGo sound pressure level gain at resonance for a resonator,

dB, Eq. (8-67)

LI acoustic intensity level, dB

Nomenclature 517

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LN energy-equivalent pressure level during the nighttime,

dBA, Eq. (6-8)

LNP noise pollution level, dBa (NP), Eq. (6-10)

Lp sound pressure level, dB

LSIL speech interference level, dB

LTr transmissibility level, dB, Eq. (9-104)

Lv acoustic velocity level, dB

LW sound power level, dB

_L1;_L2 additional equivalent lengths, m or ft, Eqs (8-8) and

(8-10)

m mass flow rate of cooling water, kg/s or lbm/sec, Eq.

(5-32)

mass flow rate of gas, kg/s, Eq. (5-57)

mass being accelerated, kg or lbm, Eq. (8-1)

unbalance mass, kg. or lbm, Eq. (9-111)

m ј S2=S1 muffler area ratio, Eq. (8-123)

m ј 2_ energy attenuation coefficient, Np/m

M molecular weight, kg/mol or lbm/lbmole, Eq. (5-38)

mass of vibrating system, kg or lbm

Ma molecular weight of air, kg/mol or lbm/lbmole, Eq.

(5-38)

mass of vibration absorber, kg or lbm, Eq. (9-133)

MA acoustic mass, kg/m4 or lbm=ft4

MS ј _wL specific (surface) mass, kg/m2 or lbm=ft2

MF magnification factor, Eq. (9-78)

n integer

number of sound wave reflections, Eq. (7-26)

exponent in Eq. (8-181)

nr rotational speed, rev/sec or rpm

N Fresnel number, Eq. (7-91)

number of cycles, Eq. (9-50)

Nb number of blades for a fan, Eq. (5-12)

Nd number of train passbyes during the daytime

ND number if airplane flights during the daytime, Eq. (6-

18)

Ne effective noy value, Eq. (6-13)

NEF number of effective airplane flights, Eq. (6-18)

Nmax largest noy value, Eq. (6-13)

Nn number of train passbyes during the nighttime

NN number of airplane flights during the nighttime, Eq.

(6-18)

No base composite noise rating, dB, Table 6-10

518 Appendix E

Copyright © 2003 Marcel Dekker, Inc.

Nr number of rotating blades

Ns number of stationary blades

NS Strouhal number, Eq. (5-65)

Nt number of tubes, Eq. (8-83)

NCB balanced noise criterion

NED noise exposure dosage, Eq. (6-3)

NEF noise exposure forecast, dBA

NRC noise reduction coefficient, Sec. 7.1.2

pрx; tЮ instantaneous acoustic pressure, Pa or lbf=ft2

pm peak amplitude of the acoustic pressure, Pa or lbf=ft2

pmax amplitude of the acoustic pressure, Pa or lbf=ft2

prms or p root-mean-square acoustic pressure, Pa or lbf=ft2

ps pitch of spring coils, m or in

P pressure rise across a fan, Pa or in H2O, Eq. (5-11)

P1 absolute pressure at the valve inlet, psia, Eq. (5-44)

Po ambient pressure, Pa or lbf=ft2

Ps surface pressure, Pa or psi

Pv vapor pressure, Pa or psia, Eq. (5-52)

PW wetted perimeter, m or ft, Eq. (5-61)

Pr ј cp=kt Prandtl number

_P pressure drop across a valve, Pa or psi, Eq. (5-43)

Q directivity factor, Eq. (2-13)

volumetric flow rate, m3/s or ft3/min, Eq. (5-11)

QA acoustic quality factor, Eq. (8-48)

Qg gas flow rate, scfh (standard cubic feet per hour), Eq.

(5-48)

QM mechanical quality factor

r radial distance, m or ft

r ј f =fn frequency ratio, Eq. (9-76)

r_ characteristic distance, m or ft, Eq. (5-34)

r_ ј рSw=2_Ю1=2 characteristic distance, m or ft, Sec. 7.5

ro reference distance for traffic and train noise, (30 m)

rv boundary layer ratio, Eq. (8-32)

R specific gas constant, J/kg-K or ft-lbf=lbm-8R

room constant, m2 or ft2, Eq. (5-7)

R1 specific flow resistance per unit thickness, rayl/m, Eq.

(8-165)

RA acoustic resistance, Pa-s/m3 or lbf sec/ft5

Rb room constant including a barrier, m2 or ft2, Eq. (7-

95)

Re effective flow resistance per unit thickness, rayl/m,

Eq. (8-165)

Nomenclature 519

Copyright © 2003 Marcel Dekker, Inc.

RE electrical resistance, _

RM mechanical resistance or damping coefficient, N-s/m

or lbf -sec/ft

RS specific acoustic resistance, rayl ј Pa-s/m or lbf -sec/

ft3

RS1 specific acoustic resistance for one screen, rayl ј Pas/

m or lbf -sec/ft3

Re real part of a complex quantity, Eq. (4-21)

RH relative humidity, Eq. (4-230)

S surface area, m2 or ft2

vehicle speed, km/h, Eq. (5-75)

S50 values of TL for the STC-50 curve, dB, Table 4-4

Sb surface area of one side of a barrier, m2 or ft2, Eq. (7-

95)

SF floor area, m2 or ft2, Eq. (7-37)

SL surface area of lining material in a plenum chamber,

m2 or ft2

So total surface area of a room, m2 or ft2

Sw surface area of a wall, m2 or ft2

t time, s

thickness of pipe wall, m or ft, Eq. (5-43)

fraction of the time that a given noise level occurs,

Eq. (6-11)

t1 time between sound wave reflections, s, Eq. (7-22)

T absolute temperature, K or 8R

OSHA permissible time of exposure, h, Eq. (6-2)

T1 absolute temperature at the valve inlet, K or 8R, Eq.

(5-48)

T60 vibrational reverberation time, s, Eq. (6-58)

TL total length of railroad cars, m, Eq. (5-81)

Tr reverberation time, s

Tt total length of the train, m, Eq. (5-88)

TL transmission loss, dB, Eq. (4-90)

TLn transmission loss for normal incidence, dB

TLP plateau transmission loss, dB, Table 4-1

Tr transmissibility, Eq. (9-100)

u rms acoustic velocity, m/s or ft/sec

velocity, m/s or ft/sec, Eq. (5-64)

uрx; tЮ instantaneous acoustic velocity, m/s or ft/sec

U ј Su acoustic volume velocity, m3/s or ft3/sec

Ut blade tip speed, m/s or ft/sec, Eq. (5-21)

v velocity, m/s or ft/sec

520 Appendix E

Copyright © 2003 Marcel Dekker, Inc.

V volume, m3 or ft3

vehicle volume, vehicles/h, Eq. (5-75)

train speed, m/s, Eq. (5-81)

VрtЮ velocity of a panel, m/s or ft/sec, Eq. (4-137)

W acoustic power, W

dimension used in predicing the NEF contours, Sec.

6.9

x linear coordinate or distance, m or ft

X equivalent number of passbyes, Eq. (5-86)

XрtЮ displacement of a wall or panel, m or ft

XA acoustic reactance, Pa-s/m3, Eq. (8-15)

Xm peak amplitude of motion, m or ft

y linear coordinate or distance, m or ft

yj mole fraction of the jth component in a mixture, Eq.

(4-226)

ymax maximum amplitude of vibratory motion, m or in

yP peak-to-peak amplitude of vibratory motion, m or in

Y porosity

YM ј 1=ZM mechanical admittance or mobility,m/N-s or in/lbf -sec

z linear coordinate or distance, m or ft

complex number, Eq. (4-21)

z_ complex conjugate, Eq. (4-65)

ZA acoustic impedance, Pa-s/m3

ZAb acoustic impedance of side branch, Pa-s/m3

Zo ј _oc characteristic impedance, rayl ј Pa-s/m

ZM mechanical impedance, N-s/m or lbf -sec/in

Zs ј p=u specific acoustic impedance, rayl ј Pa-s/m

Greek letters:

_ surface absorption coefficient

attenuation coefficient Np/m, Eq. (4-207)

__ average surface absorption coefficient

_ function in Eq. (8-87)

function defined by Eq. (9-109)

_ ј a=b panel aspect ratio

_ function in Eq. (8-94)

_ ј cp=cv specific heat ratio

_ ј рL10 _ L90Ю difference, dBA, Eq. (6-12)

_ logarithmic decrement, Eq. (9-48)

dynamic deflection, m or in, Example 9-11

_f diameter of fibers, mm, Eq. (8-180)

_ ј S50 _ TL difference, dB, Eq. (4-193)

Nomenclature 521

Copyright © 2003 Marcel Dekker, Inc.

_ decay rate, dB/s, Eq. (9-55)

_1;_2;_3 vehicle noise adjustment factors, dB, Eqs (5-79) and

(5-80)

_tc turbocharger adjustment factor, Eq. (5-82)

" eccentricity, m or in, Eq. (9-110)

_ damping ratio, Eq. (9-25)

_ damping coefficient or energy dissipation factor

_ angular coordinate

function in Eq. (5-48)

phase angle, Eq. (9-85)

_cr critical angle of incidence, Eq. (4-105)

_ effective elasticity coefficient, Pa or lbf=ft2

_ wavelength, m or ft

_b wavelength of bending waves, m or ft, Eq. (7-74)

 viscosity, Pa-s or lbm=ft-sec

 ј Ma=M mass ratio for a vibration absorber, Eqs (9-140) and

(9-141)

_ Poisson’s ratio, Eq. (2-3)

_ ј S3=S1 muffler area ratio, Eq. (8-122)

_ acoustic particle displacement, m or ft

_ density, kg/m3 or lbm=ft3

_c bulk density of cork, kg/m3 or lbm=ft3

_f bulk density of felt, kg/m3 or lbm=ft3

_L density of liquid in Eq. (5-56)

_m bulk density of acoustic material, kg/m3 or lbm=ft3

_o density at atmospheric pressure, kg/m3 or lbm=ft3

_w density of the solid wall, kg/m3 or lbm=ft3

density of water in Eq. (5-57)

 Poisson’s ratio, Eq. (4-152)

standard deviation, dBA, Eq. (6-11)

dissipative muffler attenuation coefficient, Np/m

_ ј 1=f period, s

_ ј CD=_oc2 relaxation time, s, Eq. (4-201)

_ phase angle for transmissibility, Eq. (9-105)

             phase angle

pressure ratio, Eq. (5-52)

            s structure factor, Eq. (8-169)

_ distance from the interface to the overall neutral axis,

Eq. (4-180)

ratio defined by Eq. (8-165)

phase angle, Eq. (9-127)

1 ratio defined by Eq. (8-171)

522 Appendix E

Copyright © 2003 Marcel Dekker, Inc.

рhЮ quantity defined by Eq. (9-151)

o ratio defined by Eq. (8-167)

рxЮ; рrЮ amplitude function, m or ft

! ј 2_f angular frequency, rad/s

!a undamped natural frequency for vibration absorber,

rad/s

!d damped natural frequency, rad/s, Eq. (9-36)

!n undamped natural frequency, rad/s

_ ј !a=!n frequency ratio, Eq. (9-144)

Subscripts:

in denotes incident quantity

n denotes normal incidence

ref denotes a reference quantity, pref ј reference acoustic

pressure

tr denotes transmitted quantity

Nomenclature 523

Copyright © 2003 Marcel Dekker, Inc.