SOUND PROPAGATION IN THE ATMOSPHERE 
Annual changes in the travel-time curves (Fig. 12), 
and the annual period of the radius of the zone of 
abnormal audibility, are caused by (1) annual changes 
250 
| 150 Ae | 
ae 
La 
4 
O° 
Net Nnner| sounpary (0) 
FEB|MAR 
100 O 
50 APR|MAY [JUN | JUL |AUG ce NOV|DEC | JAN |FEB|MAR 
Fig. 10—Yearly period of the distance from the source at 
which the first ring of audibility begins (circles and thin curve) 
and of the distance of the maximum number of reported obser- 
vations (dots and thick curve) based on data collected by 
Wegener [28, 29]. 
in the speed and direction of the wind, or (2) an mcrease 
in temperature above the value near the ground at ele- 
vations varying, in central Europe, between about 30 
km in late winter and 40 km in late summer. Hither (1) 
ALTENLUNNE 
98,43 km 
173579135791 
UFFELN 
128,75 km 
2% 680246802 
{ Beas 
Fre. 11a.—Direct sound waves, recorded by Kihl’s undograph, 
showing dispersion. (After Schulze [27].) 
or (2) or both operating jointly may produce this effect. 
Since the travel times for the rays arriving in the second 
abnormal zone were always close to twice the travel 
time at half the distance in the first zone (Fig. 12) it 
was concluded that the second ring is produced by 
rays reflected at the surface of the earth [11, 29]. 
Similarly, the following zone (travel-time curve ¢ in 
Fig. 12) is probably due to twice-reflected waves. Still 
later phases may be due to waves which left the ground 
under too small an angle of incidence to be turned back 
in the warm layer near 55 km, passed upward into the 
colder layer above, and finally were turned back (Fig. 
14) in the layers at an elevation about 100 km [5], 
where the temperature increases beyond that near 55 
km. 
Calculations of the temperature in the part of the 
stratosphere in which the sound waves are turned down 
to produce the first abnormal zone can be made as 
follows [10, 11]. First, equation (7) is used to calculate 
the sound velocity in the troposphere, and possibly in 
the lower part of the stratosphere. Equation (17) gives 
373 
the angles of incidence correspoading to the travel-time 
curve (b in Fig. 12); usually they change little with 
distance. Equation (14) gives the horizontal distance 
igh aint 
Fic. 116.—Records of sound waves at a distance of about 
200 km from the source at three points (distances from each 
other about 450, 910, and 845 m, respectively) at different times 
between July 21, 1927,6:46 p.m. and July 22, 1:26 a.m.; source 
near Juterbog, recorded near Wurzbach, Thiiringen, in Ger- 
many. (After Meisser [19].) 
corresponding to the ray section between the ground 
and the level for which the sound velocity has been 
calculated, and equation (16) the corresponding travel 
time. Twice these distances and times are subtracted 
ee | fav 17,1928 
DECEMBER 19, 1929 
2000 
1500 
T (SEC) —> 
fo) 
fe} 
°o 
500 
fo} 200 te} 200 400 
QO(KM) —> 
Fra. 12.—Travel-time curves from explosions near Jiiterbog, 
Germany, in summer (July 17, 1928) and in winter (December 
19, 1929). Curves a, b, c, and d apply to the first, second, third, 
and fourth zones of abnormal audibility, respectively. (After 
Gutenberg [{10].) 
