PHYSICS: A. G, WEBSTER 
Case 1. 0- = o-Q^c". (Change units so that ^ = 1) 
d^X n dX 
dx^ X dx 
-^X^O 
dx X dx 
We have 
Examples. 
p = J n-i WA 
n = 0, 
n-l 
2 
X =J 
n = 2, 
n±i 
2 
M+1 
2 
281 
(34) 
(35) 
J^(x) = sin x/V X, Jsi^) = sin x/x^ - cos /xV x, 
2 2 
3 
J I (x) = COS x/y/x'j J _3 (x) = — sin xj'sTx — cos xj^^ 
2 2 
These include the straight cylinder, the straight cone, and the purely hyper- 
bolic horn. In the latter case we have figure 5, where xi, is the bell. If the 
horn is closed at xi we have 
Z2 = CO 
„ ,2(1 ^ (sin ^/ + ^:^£;i COS ^/) iSxi 
Zj\ = ck <- i>= — - = 
K.C l-K ) c <Tok sin kli 
and if we put ^ = kl 
ctni=pi-A-;, 
Ic Xi ^ 
(36) 
which may be easily discussed graphically. 
On the other hand if the horn is open at X2 we have 
tan 
(37) 
These formulae were confirmed experimentally by my then assistant Dr. H. 
K. Stimson in 1915 on a coach-horn, a trombone, and a phonograph horn, with 
the following results: 
For the coach-horn 
For the trombone 
f Closed, 
\Open. . 
f Closed, 
\Open. . 
For the phonograph IqI^^j!^^ 
CALCULATED 
OBSERVED 
177 
181 
254 
202 
286 
305 
418 
432 
311 
304 
329 
415 
