Acoustics of a Nonhomogeneous Moving Medium Page: 68 of 202

                                
NACA TM 1399

the sound drops with increasing distance, the damping coefficient a
being equal to 1.5 to 2.2 decibels at 100 meters8. Sieg does not find
any dependence of the coefficient a   on the frequency. It should be
borne in mind, however, that the accuracy of Sieg's observations is not
large; the directional characteristics of the source were not taken into
account, and the conditions under which the points for the various
frequencies were taken were not identical. For this reason this result
doe. not appear entirely reliable; it gives rather the order of magnitude
of a which in the interval 250 to 4000 hertz does not change.
In the case of a strong gusty wind the coefficient of damping
decreases, reaching a magnitude of 5 to 9 decibels at 100 meters (for
a wind with gusts of 7 to 17 m/sec). Under these conditions the
dependence of a   on the frequency becomes more marked, a   being equal
to 5 decibels for 250 hertz, 8 decibels for 2000 hertz, and 9 decibels
for 4000 hertz (at 100 m). Under the same conditions, fading is observed;
the fluctuations of the intensity attain 25 decibels. Both these effects
are explained without forcing by the theory of the propagation of sound
in a turbulent flow (refs. 28 and 29). In considering the propagation
of sound in a turbulent flow, it is first of all necessary to bear in
mind that those fluctuations of the velocity of the stream having the
scale  I which is considerably greater than the length of the sound
wave   X do not lead to the dissipation of the sound. They bring about
only changes in the shape of the rays and therefore a general fluctuation
of the sound intensity at the location of the receiver (fading). The
effect of these large-scale pulsations may be considered by the method
of geometrical acoustics. Hence the velocity of a turbulent flow must
be decomposed into two components   v (macrocomponent) and  u (micro-
component):
q   ((2.89)
U         ei(q,   U(dQ())
q<q0
where  v  includes the mean velocity of the flow   v0. The magnitude
qO = k/ , where  k = 2r/X, is the wave number of the sound wave and   p
is a nondimensional number >>1. The dissipation of sound from a
parallelepiped  L3  where  L> X  and  L< t/q0  will now be considered.
8There is here subtracted the molecular absorption (Kneser effect
with account taken of the humidity of the air). It has a considerable
value starting with frequencies of 1000 hertz. The classical absorp-
tion due to the viscosity and the heat conductivity is of significance
only for frequencies greater than 10,000 hertz.

60