' s W-t 
( ./• 
ACOUSTICS. 
XM 
through the point B. 
sums of the right 
Now if the several 
lines A C -)- C B, 
AD -(- DB, A E + B B, AG-|-GB, 
AH + Hli, AT + TbT&c., be all equal 
to each other, it is obvious that the pulses 
propagated from A to these points, and 
again, from these points to B, will all ar- 
rive at B at the same instant, according to 
the second principle ; and, therefore, if the 
hearer be in that point, his ear will at the 
same instant be struck by all these pulses. 
Now it appears from experiment, that the 
ear of an exercised musician can alone dis- 
tinguish such sounds as follow one another 
at the rate of 9 or 10 in a second, or any 
slower rate : and therefore, for a distinct 
perception of the direct and reflected sound, 
there should intervene the interval of itli 
of a second ; but in this time sound de- 
scribes 1 ~, or 127 feet nearly. And 
j 9 : . , 
therefore, unless the sum of the lines drawn 
from each of the obstacles to the points A 
and B exceeds the interval AB by 127 
feet, no echo will be heard at B. Since 
the several sums of the lines drawn from the 
obstacles to the points A and B are of the 
same magnitude, it appears that the curve 
passing through all the points, C, D, E, F, 
G, H, I, &c. will be an ellipse. Hence all 
the points of the obstacles which produce 
an echo, must lie in the surface of the ob- 
long spheroid, generated by the revolution 
of this ellipse round its major axis. See 
Conic Sections. As there may be several 
spheroids of different magnitudes, so there 
may be several different echoes of the same 
original sound. And as there may happen 
to be a greater number of reflecting points 
in the surface of an exterior spheroid than 
in that of an interior, a second or a third 
echo may be much more powerful than the 
first, provided that the superior number of 
reflecting points, that is, the superior num- 
ber of reflecting pulses propagated to the 
ear, be more than sufficient to compensate 
for the decay of sound which arises from its 
being propagated through a greater space. 
This is finely illustrated in the celebrated 
echoes at the lake of Killarny, in Kerry, 
where the first return of the sound is much 
inferior in strength to those which immedi- 
ately succeed it. From what has been laid 
down it appears, that, for the most powerful 
echo, the sounding body should be in one 
focus of the ellipse, which is the section of 
the’ echoing spheroid, and the hearer in the 
other. However, an echo may be heard in 
other situations, though not so favourably; 
as such a number of reflected pulses may 
arrive at the same time at the ear as may 
be sufficient to excite a distinct perception. 
Thus a person often hears the echo of his 
own voice ; but for this purpose he should 
stand at least 63 or 64 feet from the reflect- 
ing obstacle, according to what has been 
said before. 
If a bell, a, fig. 5, be struck, and the un- 
dulations of the air strike the wall c d in a 
perpendicular direction, they will be re- 
flected back in the same line ; and if a per- 
son be situated between a and c, as at x, he 
would hear the sound of the bell by means 
of the undulations as they went to the wall, 
and he would hear it again as they came 
back, after the reflection, which would be 
the echo of the sound. So a person stand- 
ing at x might, in speaking in the direction 
of the wall cd, hear the echo of his, own 
voice. But in both cases the distance cx 
must be 63 or 64 feet. If the undulations 
strike against the wall obliquely, they will 
be reflected off obliquely on the other side ; 
if, for instance, a person stand at m, and 
there be any obstacle between that place 
and the bell, so as to prevent him hearing 
the direct sound, he may nevertheless hear 
the echo from the wall cd, provided the di- 
rect sound fall in that sort of oblique direc- 
tion so as to force the reflected undulations 
along the line cm. 
At the common rate of speaking, we do 
not pronounce above three syllables and a 
half, that is, seven half syllables in a second; 
therefore, that the echo may return just as 
soon as three syllables are expressed, twice 
the distance of the speaker from the le- 
flecting object must be equal to 1000 feet ; 
for as sound describes 1142 feet in a second, 
|ths of that space, that is lOOO feet nearly, 
will be described while six half, or tlnee 
whole, syllables are pronounced; that is, 
the speaker must stand near 500 feet from 
the obstacle. And, in general, the distance 
of the speaker from the echoing surface, for 
any number of syllables, must be equal to 
the seventh' part of the product of 1142 feet 
multiplied by that number. In churches 
we never hear a distinct echo of the voice, 
but a confused sound, when the speaker 
utters his words too rapidly; because the 
greatest difference of distance between the 
direct and reflected courses of such a num- 
ber of pulses as would produce a distinct 
sound is never in any church equal to 127 
feet, the limit of echoes. But though the 
first reflected pulses may produce no echo, 
both on account of their being too few m 
■hbH 
