16.4 |
Letter Symbols, Notations, and Units |
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16.4 Letter Symbols, Notations, and Units |
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Roman-Letter Symbols |
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a |
Acceleration |
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A |
Area |
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A |
Equivalent-absorption area |
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A |
Effective area (area perpendicular to particle velocity) |
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b |
Breadth, width, also: substitution for βd cos δ |
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B |
Magnetic-flux density |
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B |
Bending stiffness |
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c |
Sound-propagation speed in the free field (speed of sound) |
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cb |
Propagation speed of a bending wave |
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c |
Sound-propagation speed in an exponential horn |
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cp |
Specific heat capacity at constant pressure |
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cv |
Specific heat capacity at constant volume |
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C |
Capacitance |
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C |
Capacitance load (capacitance per length) |
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DDielectric-displacement density
Di Insertion loss
e Piezoelectric coefficient
EElectric field strength
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f |
Frequency |
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fc |
Coincidence frequency |
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F |
Force |
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g |
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Product of sound pressure and radius, g = p r |
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G |
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Electric conductance |
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G |
Conductance load (conductance per length) |
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h |
Length, height |
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h(t) |
Impulse response |
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H (ω) |
Transfer function |
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i |
Electric current |
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I |
Sound intensity (sound power per area) |
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j |
Unit of the imaginary numbers (j2 = −1) |
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JN |
Bessel function of the first kind, order N |
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k |
stiffness |
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kf |
Fresnel number |
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K |
Compression module, K = 1/κ |
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l |
Length |
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L |
Inductance |
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L |
Inductance load (inductance per length) |
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LI |
Sound-intensity level |
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Lp |
Sound-pressure level |
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LP |
Sound-power level |
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m |
Mass |
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ma |
Acoustic-mass load (acoustic mass per length) |
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M |
Magnetic-field-transducer coefficient |
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n |
Compliance |
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na |
Acoustic-compliance load (acoustic compliance per length) |
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N |
Electric-field-transducer coefficient |
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16 Appendices |
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Roman-Letter Symbols … Continued |
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p |
Sound pressure |
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P |
Power |
Pn |
Legendre polynomial |
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Pm |
Legendre function |
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n |
Active (resistive) power |
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P |
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q |
Volume velocity |
q0 |
Source strength |
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qm |
Mirror-source strength |
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q |
Source-strength load (volume-velocity per length) |
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Q |
Sharpness-of-resonance factor (quality factor), also: reactive power |
Q el |
Electric charge |
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r |
Damping (fluid damping), also: distance, also: radius |
r c |
Critical distance |
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r rad |
Radiation resistance |
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R |
Sound-reduction index, also: electric resistance, also: radius |
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R |
Reflectance |
R |
Electric resistance load (resistance per length) |
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RI |
Isolation index |
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s |
Strain |
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s |
Complex frequency, s = α˘ + j ω |
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S |
Standing-wave ratio, also: area of a wall, window, etc. |
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T |
Reverberation time, also: temperature, also: torch, also: period duration |
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Torch per width |
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Tip |
Transfer coefficient of a transducer, driven as sender |
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Tpu |
Transfer coefficient of a transducer, driven as receiver (sensitivity) |
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Tpp |
Sound-pressure-transfer factor |
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Tup |
Transfer coefficient of a transducer, driven as a sender |
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u |
Electric voltage |
U |
Perimeter |
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v |
Particle velocity |
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V |
Volume |
W |
Energy, or work |
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W |
Energy load (energy per length) |
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W |
Energy density (energy per volume) |
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x ff |
Far-field distance |
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Y |
Admittance, Y = 1/Z |
Ya |
Acoustic admittance |
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Yf |
Field admittance |
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Y mech |
Mechanic admittance (mobility) |
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Z |
Impedance |
Z0 |
Terminating acoustic impedance of a tube |
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Za |
Acoustic impedance |
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Zf |
Field impedance |
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ZL |
Line impedance (acoustic impedance of a tube) |
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Z mech |
Mechanic impedance |
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Z rad |
Radiation impedance |
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Zw |
Characteristic field impedance of a medium (wave impedance) |
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Zwall |
Wall impedance (surface impedance) |
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16 |
Appendices |
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Specific Mathematical Notations and Terms |
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zˆ |
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Amplitude, peak value |
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z |
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Complex amplitude—note that the on top of z is omitted |
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Time average, e.g., used for active power and active intensity |
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z |
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−→ |
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Vector |
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z |
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−→ |
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z |
Magnitude of a vector |
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z |
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| z |, z |
Magnitude of a complex amplitude |
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z |
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z |
Magnitude of a complex vector |
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Re { z } |
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Real-part operator, Re { z } = Re {a + jb} = a |
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z− |
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Steady component of a function z(t) = z− + z |
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z |
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Alternating component of a function z(t) = z− + z |
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z → |
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Forward-propagating wave component |
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z |
← |
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Backward-propagating wave component |
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Root of the time average of z(t) |
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(root mean square) |
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z rms |
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For periodic functions of period duration T we have |
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1 |
T |
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2 |
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z rms = |
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T |
0 |
z(t) |
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dt , of sinusoidal functions z rms |
= zˆ/ |
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◦ • ... Fourier transform
... Proportional
Coefficient ... Multiplier of dimension = one
Degree ... Multiplier of dimension one and values of 0–1 (0–100%)
Factor ... Multiplier of dimension one
Units )
Basic SI-units |
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m |
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Meter ... unit of length |
kg = Ns2/m |
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Kilogram ... unit of mass |
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s |
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Second ... unit of time |
A |
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Ampere ... unit of electric current |
Some often used SI-derived units |
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Hz = 1/s |
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2 |
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Hertz ... unit of frequency |
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N |
= |
(kg m)/s |
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Newton ... unit of force |
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2 |
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Pa = N/m |
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Pascal ... unit of pressure |
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W = V A = (N m)/s |
Watt ... unit of power |
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V = W/A |
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Volt ... unit of electric potential difference, voltage |
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C = A s |
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2 |
/W |
Coulomb ... unit of electric charge |
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= V/A = V |
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Ohm ... unit of electric resistance to direct current |
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F = C/V |
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Farad ... unit of capacitance |
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H = (V s)/A |
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Henry ... unit of self-inductance |
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T = N/(A m) |
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Tesla ... unit of magnetic flux |
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) All units used in this book are consistent with the SI-system (système international d’unités)