In view of the interest which is being taken in the effect of wind on the propagation of sound it may be worth while to recall the form which Döppler's principle assumes when a wind is blowing

Bateman, Harry

English

Caltech Authors - Main

SEPTEMBER, 1917. 
. I  
Decade departure 
L 
MONTHLS WEATHEB REVIEW. 
................. 
44 1 
TABLE L-Solor radiation intensities during Septnnba, i9lY-Contd. 
Santa Fer N. Mer. 
................ 
1 
Sun's senlth distance. 
0.0' 1 48.8' I 80.0' I 88.5" I 10.7' 1 73.6' I 75.7. I 77.4' I 78.7. 179.8' ~ - -  \ Ai  mass. Data. 
....... ....... ....... 
....... 
12 .... ..... 
13 ....... ....... 
15.. ............. ....... ....... 
22 ....... 
tal. tal. cat. . CUI. I  ea^. M I .  
1. Ill , 1.04 0.9s u.132 0.87 (1.82 
1.118 1.01; 1.00 ....... ' ............. 
1.131 i . m l  i . m /  n . w /  0.911 ...... 
..................... I.. o,$;  ...... 1 .............. 
1.01 o . w l  0 7 9 1  ..__.. 
i.a%: 1.00 ........................... 
............................ 0.951 0.91 
1.91 1.18 1.14 1 i . i q  1 1 . w  ! 0.91 
1.17 1.Mi 0.9; O.&a ....... I ...... 
i . ? ~  1.14 1 . i ~  1.021 0.97 I n.93 
i l l  M o n t h l y  I 
Departure j , i I 0 ;  I 
hum 5 w r  
noimnt .._.. : - -n .nb -0.03 '-.n.os -0.04 .-o.U3 !-u.o4 I-0.03 /--o.uct I-u.oaj-n.o3 
means .__._ : ( I . 4 5 j i  1.38'  1.8A 1 . 2 1 ;  l . l J (  1.011 1.021 0 . 9 5 1  0 . 9 2 )  U.89 
sept.2q P. Sf.  p j i  .............. ' 1.52 1.4s 1 . 3 t i :  1.9' 1.2'1 1.131 .............. ! ...... 
Y on t h 1 y ' I  means ............. t m j j  il.481 ( 1 . A  ( i . zo , i  (1.214 ,I.lsii ....... ! .............. 
13 lromb e pa1 r tu enr rc I ' : i l ! j  
uormsf .... i ....... ;+U.O2 i+0.07 +O.U5 /+0.09 I+U.U7 I+U.Q I ....... i ....... i ...... 
I__ . _ .. .. -. ..... - .. __ -. __ ._ _- ...  ._ _ _  ...... __ . .-.  - 
TABLE 9.- Ikpor pressures at pyrlicliometrie stations on days when solar 
radiatiou intensities ume memilred. 
___ - - 
-- __ 
1917. mm. mna. 
sept.3 7.04 5.79 
7 9.47 7 14.60 4 6.50 6.50 
11 5.16 5 10.59 5 7.57 0 . x  
12 z.57 11 7.57 ti b.7G G.i6 
13 8.87 13 11.81 i 6.02 S.81 
17 9 .m 17 11.35 12 9.83 9 $3 
19 10.59 21 9.m 15 4.75 5 . S  
22 9.47 19 7.32 ti. 3) 22 10.07 
L! !I..% 23 7.87 7.32 6.71; 
a4 9.47 28 3.81 3.61 
27 5.79 .................... 
-- 
1917. mm. 
6ept.5 15.11 
.--- 
1917. mm. 
Eept. 4 9.14 
18 8.45 18 9.47 13 5.48 I 1 0 : s  
p 
.................... ! 
j .................... ' ' (  I I .' -____ 
IUrani-c-~lories per srliiare ernt.lmeter 01 hmizonlal 
~ a y  01 month. I- 
Wash- I ington. 
191;. calories. 
a p t .  1 ................ 
2 ............... ! E 
3.. .............. 
.I ................ I 
i) ................ 
G ................ 
7. ............... 
9.. 
.............. .............. i a.. ............... 10. 11 ................ 12 ................ 13.. .............. 
14. ............... 
15 ................ 
16.. .............. 
17 ................ 
I8 ................ 
19.. ............ .-I 
20.. .............. I 
Decade departure.. .... 
 
 ....  352 
6 350 
113 
 .... 319 
 .... 11; 
 400 
524 
  450 
 ..... 235 
101 
273 
5OG 
 ... . I 436 
505 
.... 
 .. .. .. .... ..I 33; 
_- 
dadison 
21.. ............. .I .............. I 22.. 23.. .............. 
%I ................ i 
25.. .............. ae. ............... 
27.. .............. ae.. .............. as ................ I 
30 ................ ; 
31. ......... ......I.. ... 
316 
432 
.m 
216 
243 
&a9 
409 
208 
336 
431 
...... 
calorie.. 
330 
267 
471 
233 
6 7  
53 
429 sa 
549 
559 
353 
197 
403 
349 
413 
394 
417 
258 
99 
43f8 
429 
JZ! 
411 
361 
94 
412 
419 
412 
310 
&a 
........ 
....... 
_____-- 
Depart- from 
normal. 
WSh- 
ingtm. 
ealosie.4. 
-217 
-47 
-55 
100 
-23 
-288 
--so 
-346 
-279 
5 
176 
135 
67 
-150 
-285 
-111 
124 
75 
59 
-37 
-56 
I 
-64 
-148 
-118 
71 
54 
-143 
-12 
91 
......... 
......... 
......... 
......... 
dadison 
WlOtlC.3. 
-64 
01 - 121 
86 
- la1 
Qa 
-321 
(wl 
-34 
187 
1% as 
- 152 
58 
7 
74 
58 
54 
- 71 
-236 
114 
111 
107 
loa 
86 
-210 
112 
123 
120 
22 
-
........ 
....... 
........ 
....... 
Iarc.] 
Kxeess or de5cIency 
ilneefirotofmonth. 
.- 
Wash- 
ington. 
calories. 
-217 
-264 
-319 
-219 
- a 2  
-530 
-610 
--853 
-1 !a37 
-1:a32 
-1,056 
-1'289 
-1'201 
- 1 : m  
- I ' m  
-1'502 
-1'5x1 
-1'532 
-921 
-854 
-1 Mu 
-1:400 
-1 276 
-1'142 
s3 
-1 !za5 
-1:236 
-1 381 
-1'431 
-1'397 
-1:441 
-262 
-5,981 
-5.6 
dsdlson. 
calorled. 
-64 
-3 
-124 
- 45 
-18s 
-90 
-411 
-351 
- 43% 
-242 
-213 
-365 
-307 
-300 
--Pi 
-1W 
-84 - 1.55 
-381 
57 
-3ji 
-1bi - .I9 
54 
140 - 70 
42 
Mi5 2s 
:w7 
688 
1,m 
1.6 
........ 
5</. .~.5 sC/- ST6 
DePPLEB'S PRINCIPLE FOB A WINDY ATMOSPHEBE. 
By HARRY BATEMAN, Ph. D. 
Ilrated: 730 South Lake Avenue. Pasadena, Cal.. Oct. 15,1917.1 
In view of the interest which is bein taken in the effect 
of wind on the propagation of souns it may be worth 
while to recall the form which Doppler's principle assumes 
when a wind is blowing. 
If the observer is nioving wit,li velocity 'u., the source of 
sound with velocity ,v, and the wind with velocity V, 
all measured in the same direct>ion, then in the case of 
sound wave3 moving in the opposite direction and 
originating at t.he source with frequency v t,he observed 
frequency is 
(1) 
6 -  I ' + u  
0 v I ' -  T.'+.7, 1' = 
where c is the veloc.ity of sound in still tlir. 
This result, may be obtained with the ordinary form of 
Diippler's principle either by reducing the air to rest by 
snbst.ractin 
regarding tit! vclocity of sound in the moving air as c - 6: 
To prove t,he formula analytically let 11s neglect the 
variation of air-density and wind-velocity with altitude 
and assume that the wind is blowing steadily in a direc- 
tion parallel to the axis of 1: with velocity V, then the 
velocity potential 4 of sound waves propagated through 
tho air satisfies the partia.1 differontial equation.' 
t.he wind velocity T' from ,u and T'! or b 
This equation may be t,ransformed into the ordinar 
wave-equation for still air by writin x' in place of 3- d 
which is at t,lie point [ ( T I ,  v (T ) ,  f ( ~ )  at time 7 is 
The solution corresponding to sound f rom a Inoving source 
1 
4 = +f(d 
where 'T is defined by the equation 
and y is the partial derivative of t-he left-hand side with 
res ect to r .  
[X - E(7) - 17(t-- T ) I 3  + [y -v(T)la + [ Z -  f ( T ) p = 8 ( t -  T)' ,  
W t h g  
XL'=a+ut, y=o, Z = o ,  E(T)=o!+%'T, V ( T ) = O ,  f ( T ) = o ,  
where a,, a, u, v, are constants so as to have the case of a 
source and observer moving dong the same straight line 
with different constant velocities, we find that 
t (u-v*c)+a-a 
2,- V*c 7 s -  
For sound of frequency B we may write ~ Y T )  =Asira(v7 + e) 
and the observed fre uency is seen to be given by formula 
(1). The wave-lengt 7l is also 
It should be noticed that if U='L' the observed fre uency 
is the same as the natmural fre uency whateverte the 
is the same as the natural wave-length. In  sctual 
practice the horizontal wind velocity may bo different at 
the locations of the source and observer owing to vertical 
motion of the air, eddy motion, and friction. An exact 
mathematical treatment of the general problem is diflicult 
velocity of the wind. If v =  17 t ll e observed wave-length 
1 See. for instance. S. Fqifwhnra. in Bull.. Central metwrol. obs'y, Japan. Tokyo. 
11912), 2, no. 1. 
442 MONTHLY WEA 
but if. U is the wind velocity near the obseiver and V the 
wind velocity near the source of sound, the empirical 
formula 
c- u+u 
e- v+v 
may be fairly accurate. It may be worth while to test 
this formula ex erimentdy. 
naturdy complicated and is much more so when the 
variation of air density and wind velocity are taken into 
account. Experiments with sound produced in a moving 
aeroplane may indicate whether the above variations of 
atmospheric conditions with altitude have any appreciable 
effect on the observed frequemy. 
v,=v 
In the case o P an overhead source of sound the theory is 
PBOPAGATION TO GBEAT DISTANCES OF THE SOUND OF 
CANRONADE AT THE FRONT.’ I 
ci. nIQOUItDhN. 
[Rcpnntdfrom bienca .4bstroets, Sect. A, July 30, 1917, $057.1 
A cannonade produces various noises from the mouths 
of the guns and from the explosions of the shells. Some 
of these noises can reach great distances, 200 to 300 kilo- 
metera, but it is not a eed how they reach them. 
It is thus thought f sirable to cite the case of an en- 
gineer, a$ed 52, totally deaf since the age of 6 through 
cerebrosplnal meningitis. Placed at the side of a loco- 
motive whistlin , he perceived only a sudden pain of the 
drum skin, whic ceased immediate1 in spite of the con- 
tinuation of the whistling. Tor the ast 20 years if within 
1,000 to 1,500 meters of guhiire, he perceives two suc- 
cessive shocks--one transmitted by the earth, one by the 
air. The last affects the thorax particularly. Bt the 
commencement of the Somme offensive, from the out- 
ski& of Paris, when attending [attentive?], he was con- 
scious of vibration duri the cannonade; sometimes he 
would perceive only dull 5 lows, at others he would per- 
ceive something at the same instant as an ordinary hearer. 
The distance to the Somme front (130 kilometers) es- 
chded entirely the route through the air, so it must be 
by the earth; and SO also for the normal hearer, since both 
perceive it at the same time (see Science Abstracts, 1916, 
P B 
#1056).--E. H .  B[at’ton]. 
5x/. .q75 : s 3 . m  
ACCOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINEBY. 
By L. v. KINO 
[Reprf%tcdfron8 Science Abstructs, Sect. -4, July W, 1917, #jiiS.l 
The first section of this aper sketches the histor of 
fogsignal ex eriments, dw & ‘ng speciall on the wor 1 - of 
Tyndall pubLhed in 1874 in a Trinity house report. 
At about the same time experiments by Duane and 
by Jose h Henry were conducted, and were ublished in 
1874. h e  res& of fog-signal tests Carrie a out in the 
United States to the ear 1894 were published in Liver- 
more’s Report to the E ighthouse Board of that date. 
In  1901 a coinmittee of the Trinity House carried out, 
at the Isle of Wight, a series of tests under the scientific 
direction of Rayleigh and T. Matthem. For c a h  weather 
a low note (about 180 er second) was considered most 
suitable; when the win cp was contrary and the sea rough, 
~Compte~Rendua Paris Oct 2 1816 163:azmz4 * JW-.  Franklin h t . ,  Phd*el~hb,,basr., 1817,1’83: %%%6. 
,THER REVIEW. SEPTEMBER, 1017 
it  was found that a higher note penetrated farther than a 
low one. The ph ical significance of this was discussed 
while a blast is being sounded from a siren w ‘ch can be 
heard about 8 nliles awa on a good day, energy is bein 
note of a Scottish signal required 600 horsepower. Ray- 
leigh raised the question as to whether these enormous 
powers are really utilized for the production of sound or 
whether from some cause, ossibly avoidable, a large pro- 
portion may not be waritex 
The experience of French fog-si nal en ‘nears was 
summed up by C. Ribhi8re in 1908. b u s  emsasized the 
desirability of obtaining further knowledge as to the effi- 
ciency of the fogsignal a paratus. 
The second section dea F s with the production of sound 
by R special siren called the “ diaphone,” clue in its raent  
form to J. P. Nort,liey. ’rhe essential feature of ap- 
arat,us is t~ liollow cylindrical piston, which is oscillated 
foigitudinally by the “driving air,” and so opens and 
closes ports which allow n series of uffs from the “sound- 
ing air.” These puffs gin? a near F y pure tone of about 
150 per second. This sound passes t,hrough a suitable 
holm. 
Tlie bird section is occupied with the numerical rela- 
tions between sound waves and their audibility as fog- 
signals. 
The fourth section deals with the “phonometer” due to 
S .  G. Websber. This consists of a Helmholtz hollow cylin- 
drical resonating chamber, one elid of which is ierced by 
a smooth hole communicating freely with t R e atmos- 
phere, while the other has a very uniform plate of the best 
mica obtainable (such as is used in phonographs). The 
resonator is tuned to the pitch for which it is to be used as 
a detector, and the vibrations of the mica diaphragm are 
detected and measured RS follows : The mica disk carries a 
A narrow shalY tee stri is suitably held taut at both extremities in a 
fork capAle of adjustment, sild t,he st.rip has its center in 
contact with t,he steel point, so that a slight movement of 
the disk and ioint gives t,he strip a corresponding twist. 
reflected from R small concave mirror carried by the strip. 
The diaphone may be worked backward and is then 
called the ”‘phone” or standard generator. When ita 
dia hragm is made to oscillate through a known ampli- 
tu& it IS possible to calculate the numerical character- 
istics of the spherical sound waves emitted. By the use 
” and the ‘ I  phonometer” the acoustic 
Of output the o “phone any sound generator of the same pitch (such 
as violin, cornet, or human voice) may be calculated. 
Section five is on aerial sound waves of large ampli- 
tude and the discontinuity that may be expected to 
occur in their propagation. In the sixth section the 
thermodynamic estimate of acoustic efficiency is treated. 
By the use of resistance t,hermometers of iron wire one 
one-thousandth inch in diameter the temperature fall of 
the air, due to the conversion of the compressed air 
energy into sound, was measured in the diaphone. 
ments carried out near Quebec in 1913. R$aggk 
efficiency of the diaphone in one case was found to be 
nearly 6 per cent, in another a little over 8 per cent. 
Using his phonometer A. 0. Webster had previously found 
the violin, the cornet, and the human voice to have 
acoustic efficiencies of about 0.05 per cent, 0.1 per cent, 
and 1 per cent, respectively. 
‘R by Rayleigh at t r a t  time? It appears su rising that 
expended at the rate of a i out 100 horsepower. The higE 
steel point firmly clamped a t  its center. 
This twist is J etected by the movement of a beam of light 
, 
Section seven deals with the actual fog-si 
___.__ - 
al’hil. Mag.. 190% 6: 388305. 


Döppler's principle for a windy atmosphere

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Döppler's principle for a windy atmosphere

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