Units, conversion factors, and physical constants

This section contains information on units (immediately below), physical constants, conversion factors, and miscellaneous data related to air and sound.

To the list of Physics of sound subsections.

Fundamental units

Quantity

Symbol

Units

Dimensions

Time

t

Seconds

[s]

Length

 

Meters

[m]

Mass

M

Kilograms

[kg]

Charge

q

Coulombs

[q]

 Other physical quantities

Quantity

Symbol

Units

Dimensions

Weight

 

Kg-weight

[kg-m-s-2]

Force

F

Newtons (N)

[kg-m-s-2]

Velocity

v

 

[m- s-1]

Acceleration

a

 

[m-s-2]

Energy/Work

E

Joule (J)

[kg-m2-s-2]

Power

 

Watt (W)

[kg-m2-s-3]

Density

ρ

 

[kg-m-3]

Pressure

P

Pascal (Pa)

[kg- m-1-s-2]

Sound intensity

I

W-m-2

[kg- s-3]

Temperature

T

0K

-none-

Volume

V

 

[m3]

Moles

n

mol

-none-

 Electrical quantities

Magnetic field

B

Tesla = Weber-m-2

[kg-s-1-q-1]

Electric field

E

Volts-m-1

[kg-m-s-2-q-1]

Electric current

I

Amps

[q-s-1]

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Physical Constants

Updated 3/18/98 based on values provided by NIST

Constant

Symbol

Value

Units

Dimensions

Avogadro's number

N

6.0221367x 1023

mol-1

-none-

Gas constant

R=Nk

8.31451

J-0K-1-mol-1

[kg-m2-s-2]

Boltzmann's constant

k

1.380658 x 10-23

J-0K-1

[kg-m2-s-2]

Standard molar volume

V0

.0224141

m3-mol-1

[m3]

Planck's constant

h

6.62606876x10-34

J-s

[kg-m2-s-1]

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Conversion factors 

Length

1m = 3.2808 ft

1 km = .62137 mi.

1 Angstrom ≡ 10-10 meters = 3.937 x 10-9 inch

Volume

1 m3 = 1000 liters = 35.315 ft3

Mass

1 kg = 2.20462 lbs. avoirdupois

Velocity

1 m-s-1 = 3.6 km/hour = 2.2369 MPH

Force

1 Newton = 105 Dynes = .10197 kg-weight = .22481 lb-wt

1 kg-wt = 2.20462 lb.-wt = 70.93 poundals=9.80665 Newtons

Acceleration due to gravity @ sea level, 45-deg lat

1 g = 9.80621 m-s-2 = 32.1725 ft-s-2

Energy

1 Joule ≡ 1 watt-s = .10197 kg-meter = 107 ergs

Temperature

Zero 0C = 273.15 0K

72 0F = 22.2 0C = 295.4 0K

Pressure

1 atmosphere = 1.0332x104 kg-m-2 = 2116.2 lbs.-ft2 = 14.7 psi = 76 cm Hg = 1.0132x105 Pa

0.00002 Pa RMS ≡ 0 dB SPL

The theoretical limit for a sinusoidal sound wave is a minimum pressure of zero (a total vacuum) and a maximum pressure of 2 atmospheres, which is a level of 191.1 dB SPL.

1 Bar ≡ 106 Dyne-cm-2 = 105 Pa = 193.98 dB SPL

Warning! Sometimes authors define 1 Bar ≡ 1 Dyne-cm-2 = 73.98 dB SPL. A confusing aspect of this is the fact that the units of pressure are mass - length-1 - time-2, and 1 atmosphere is given in units of kg-m-2. The "kg" in the the atmosphere defintion is not mass, but the force exerted by a 1 kg mass subject to a gravatational acceleration g = 9.8062 length-time-2.

Sound intensity

Reference level ≡ 10-12 W-m-2

1 W-m-2 = 120 dB above reference, produces a pressure level of 20.7 Pa

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Miscellaneous Data

Atmosphere=78% N2, 21% O2 by volume

N2 1.2506 kg-m3 at 1 atm, 00 C

Dry air @ 200 C, 1 atm = 1.205 kg -m-3

N atomic weight 14.0067, atomic radius .74 Ang

Speed of sound 331.36 ms-1 at 1 Atm, 00C.

For other temperatures T in oC, multiply by sqrt(1+T/273.16)

Characteristic impedance of air Zo=428 rayls at 1 Atm 00C, 413.3 at 200C

Molecular constants

Average molecular velocity, air 463 m-s-1 at 200 C

N2 at 200 C, 1 atm:

Mean free path, 8.21, 9.29 x10-8 m

Collision frequency 5070 x 106 s-1

Molecular diameter 3.3 x 10-10 m

Molecular density, 2.687 x 1025 m-3

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