2.1 SPEEDOF SOUND

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Sound is defined as a pressure disturbance that moves through a material at

a speed which is dependent on the material (Beranek and Veґr, 1992). Sound

waves in fluids are often produced by vibrating solid surfaces in the fluid, as

shown in Fig. 2-1. As the vibrating surface moves to the right, the fluid

adjacent to the surface is compressed. This compression effect moves outward

from the vibrating surface as a sound wave. Similarly, as the surface

moves toward the left, the fluid next to the surface is rarefied. The vibratory

motion of the solid surface causes pressure variations above and below the

fluid bulk pressure (atmospheric pressure, in many cases) to be transmitted

into the surrounding fluid.

Noise is usually defined as any perceived sound that is objectionable or

damaging for a human. Noise is somewhat subjective, because one person’s

‘‘music’’ may be another person’s ‘‘noise.’’ Some sounds that could be classified

as noise, such as the warning whistle on a train, are actually beneficial

by warning people of potential dangerous situations.

The speed of sound in various materials is given in Appendix B. For an

ideal gas, the speed of sound is a function of the absolute temperature of the

gas:

c ј рge_RTЮ1=2 р2-1)

Copyright © 2003 Marcel Dekker, Inc.

where gc is the units conversion factor, gc ј 1 kg-m/N-s2 ј 32:174 lbm-ft/

lbf -sec2; _ is the specific heat ratio, _ ј cp=cv; R is the specific gas constant

for the gas, R ј 287 J/kg-K ј 53:35 ft-lbf /lbm-8R for air; and T is the absolute

temperature, K or 8R.

The speed of sound (or c2) in a fluid (liquid or gas), in general, is given

by:

c2 ј

_B

_ р2-2)

where B is the isothermal bulk modulus and _ is the fluid density. For

transverse (bulk) sound waves in a solid, the speed of sound is given by

(Timoshenko, 1970):

c2 ј р1 _ _ЮE

р1 ю _Юр1 _ 2_Ю_

(2-3)

where E is Young’s modulus and _ is Poisson’s ratio for the material. For

sound transmitted through a thin bar, the speed of sound expression reduces

to:

c ј рE=_Ю1=2 (2-4)

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