Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 99

The radial particle velocity in a nondirectional spherically spreading sound field is given by Euler's equation as

(3.37)

and substituting Eqs. (3.34) and (3.37) into (3.15) and then using Eq. (3.35) and time averaging gives the magnitude of the radial sound intensity in such a field as

(3.38)

the same result as for a plane wave. The sound intensity decreases with the inverse square of the distance r. Simple omnidirectional monopole sources radiate equally well in all directions. More complicated idealized sources such as dipoles, quadrupoles, and vibrating piston sources create sound fields that are directional. Of course, real sources such as machines produce even more complicated sound fields than these idealized sources. (For a more complete discussion of the sound fields created by idealized sources, see Ref. [21] and chapters 3 and 8 in the Handbook of Acoustics [1].) However, the same result as Eq. (3.38) is found to be true for any source of sound as long as the measurements are made sufficiently far from the source. The intensity is not given by the simple result of Eq. (3.38) close to idealized sources such as dipoles, quadrupoles, or more complicated real sources of sound such as vibrating structures.

Close to such sources Eq. (3.15) must be used for the instantaneous radial intensity, and

(3.39)

for the time‐averaged radial intensity.

The time‐averaged radial sound intensity in the far field of a dipole is given by [4]

(3.40)