374 
from selected observed values of the travel-time curve 
considering the calculated angles of incidence at the 
ground. This results in a travel-time curve for rays 
SOUND VELOCITY (M/SEC.) 
HELGOLAND 
APRIL 18, 1947 
ALC FROM SOUND 
ELEVATION (KM) 
-80 =60 -40 -20 0 20 40 60 
TEMPERATURE (°C) 
Fic. 13.—Temperature and sound velocity in the atmosphere 
from various sources. 
at the level where the temperature observations end. 
Equation (18) then permits the calculation of the high- 
est point H* above the level of reference reached by a 
THE UPPER ATMOSPHERE 
(Fig. 10) and of the travel times (Fig. 12) is affected by 
the yearly period of the wind, but it is caused mainly 
by the annual period of the temperature (and thus by 
the similar period of the ozone content) at elevations 
between about 25 and 60 km. Annual changes in the 
direction of the wind near and above the tropopause 
shift the whole zone in the direction of the prevailing 
wind, but cannot explain the annual expansion and 
contraction of the zones which has been observed. 
Observations of the amplitudes of sound waves 
through the stratosphere are very scarce. The maximum 
near the inner boundary of the abnormal zone results 
from the concentration of energy connected with the 
cusp of the travel-time curve at the minimum distance 
(Fig. 14) reached by the rays [11], where the very 
large values of di/dA produce a focal point according 
to equation (32). The intensity of the sound waves 
there may be so large that wmdowpanes are broken 
[14]. The records of the Helgoland explosion [4] showed 
good agreement between the observed sound-intensity 
and the energy calculated from equation (32). How- 
ever, Cox [4] has pointed out that the decrease in short 
waves relative to the long waves with increasing dis- 
tance (to be expected from the increase in absorption, 
see Fig. 3) is not confirmed by these records. The 
differences in recorded periods are relatively small and 
may be a consequence of local effects. 
In very large explosions, another group of waves is 
recorded. The best example is furnished by barograph 
records following the explosion of Krakatao in 1883; 
the pressure waves circled the earth several times, with 
DIFFERENCES BETWEEN DAY AND 
NIGHT INCREASING WITH HEIGHT 
ABSORPTION INCREASING 
RAPIDLY WITH HEIGHT 
= = —___ 
FIRST ZONE ~~ 
OF) SILENCE 
(e) A(KM)}—> 100 
Fig. 14.—Typical paths of sound waves in the atmosphere. (Hatended from Gutenberg [11].) 
given ray; the wave velocity at this pomt is equal to the 
apparent velocity at the distance where the ray arrives. 
In this way the velocity (and consequently the tem- 
perature) for a number of points in the stratosphere 
can be found as far as the temperature increases with 
height. If necessary and possible, corrections for the 
wind should be made. The upper limit of height for 
which results can be found is given either by the in- 
creasing absorption or by a decrease in wave velocity 
with height (usually as’a consequence of a decrease in 
temperature); both may be involved. Figure 13 gives a 
few results. The temperatures, calculated from the 
sound observations, agree with the observations from 
V-2 data [22] within the limits of error. 
The yearly period of the radius of the abnormal zone 
a mean velocity [24] of 314.1 m sec! (measured along 
the surface of the earth); the mean value from recorded 
sound waves travelling three times around the earth 
eastward was about 320 m sec, westward about 304 
m sec—!. The velocity of 314 m sec corresponds to a 
temperature of —28C. Similar waves with a velocity 
of 301 m sec! (not corrected for wind effect) were 
recorded at Tucson, Arizona, in southern California, 
and in Nevada [12] after the explosion of the atomic 
bomb in New Mexico in 1945. This group of waves 
followed, after many minutes, the waves discussed 
previously, and carried the largest amplitudes. At 
Pasadena, it was strong enough to record on the strain 
seismograph as a single wave having a period of about 
12 sec; apparently, the arriving pressure wave com- 
