ACOUSTICS 
the increase of the direct expansion and 
velocity of the included air. 2. The in- 
crease of the number of pulses, by in- 
creasing the points of new propagation. 3. 
The reflections of the pulses from the tre- 
mulous sides of the tube, which impel the 
particles of air forward, and thus increase 
their velocity. 
An umbrella, held in a proper position 
over the head, may serve to collect the 
force of a distant sound by reflection, in 
the manner of a hearing-trumpet; but its 
substance is too slight to reflect any sound 
perfectly, unless the sound fall on it in a 
very oblique direction. The exhibition of 
the Invisible Girl is said to depend on the 
reflection of sound; but the deception is 
really performed by conveying the sound 
through pipes artfully concealed, and open- 
ing opposite to the mouth of the trumpet, 
from which it seems to proceed. 
When a portion of a pulse of a sound is 
separated by any means from the rest of the 
spherical or hemispherical surface to which 
it belongs, and proceeds through a wide 
space, without being supported on either 
side, there is a certain degree of diver- 
gence, by means of which it sometimes 
becomes audible in every part of the me- 
dium transmitting its but the sound thus 
diverging is comparatively very faint. 
Hence, in order that a speaking-trumpet 
may produce its full effect, it must be di- 
rected in a right line towards the hearer ; 
and the sound collected into the focus of a 
concave mirror is far more powerful than at 
a little distance from it, which could not 
happen, if sound, in all cases, tended to 
spread equally in all directions. It is said 
that the report of a cannon appears many 
times louder to a person towards whom it 
is fired, than to one placed in a contrary 
direction. It must, says Dr. Young, have 
occurred to every one’s observation, that a 
sound, such as that of a mill, or a fall of 
water, has appeared much louder after 
turning a corner, when the house or other 
obstacle no longer intervened. Indeed the 
Whole theory of the speaking-trumpet would 
fall to the ground, if it were demonstrable 
that sound spreads equally in all directions. 
In windy weather it may be often observed, 
that the sound of a distant bell varies almost 
instantaneously in its strength, so as to ap- 
pear twice as remote at one time as an- 
other. Now if sound diverged equally in 
all directions, the variation produced by 
the wind would not exceed one tenth of the 
apparent distance ; but on the supposition 
VOL. I. 
of a motion nearly rectilinear, it may easily 
happen that a slight change in the direc- 
tion of the wind shall convey a sound, either 
directly or after reflection, in very different 
degrees to the same spot. 
The decay of sound is the natural conse- 
quence of its distribution throughout a 
larger and larger quantity of matter, as it 
proceeds to diverge every way from its 
centre. The actual velocity of the particles 
of the medium transmitting it appears to 
diminish simply in the same proportion as 
the distance from the centre increases : 
consequently their energy, which is to be 
considered as the measure of the strength of 
sound, must vary as the square of the dis- 
tance ; so that at the distance of ten feet 
from the sounding body the velocity of the' 
particles of the medium becomes one-tenth 
as great as at the distance of one foot, and 
their energy, or the strength of the sound, 
only one-hundredth as great. 
An echo is a reflection of sound striking 
against some object, as an image is reflected 
in a glass : but it has been disputed what are 
the proper qualities in a body for thus re- 
flecting sounds. It is in general known, 
that caverns, grottoes, mountains, and 
ruined buildings, return this reflection of 
sound. We have heard of a very extraor- 
dinary echo, at a ruined fortress near Lou- 
vain, in Flanders. If a person sung, he 
only heard his own voice, without any re- 
petition ; on the contrary, those who stood 
at some distance, heard the echo, but not 
the voice ; but then they heard it with sur- 
prising variations, sometimes louder, some- 
times softer, now more near, then more 
distant. There is an account in the Me- 
moirs of the French Academy, of a simi- 
lar echo near Rouen. It has been already 
observed, that every point against which 
the pulses of sound strike, becomes the 
centre of a new series of pulses, and sound 
describes equal distances in equal times; 
therefore, when any sound is propagated 
from a centre, and its pulses strike against 
a variety of obstacles, if the sum of the right 
lines drawn from that point to each of the 
obstacles, and from each obstacle to a second 
point, be equal, then will the latter be a 
point in which an echo will be heard. Thus 
let A, fig. 4, be the point from which the 
sound is propagated in all directions, and 
let the pulses strike against the obsta- 
cles C, D, E, F, G, H, I, & c . each of 
these points becomes a new centre of pulses 
by the first principles, and therefore from 
each of them one series of pulses will pass 
C 
