ACOUSTICS. 
sound will be the most distinctly heard. 
The augmentation of sound, by means of 
speaking-trumpets, is usually illustrated in 
the following manner : Let ABC, fig. 3, be 
the tube, BO the axis, and B the mouth- 
piece for conveying the voice to the tube. 
Then it is evident when a person speaks at 
B in the trumpet, the whole force of his 
voice is spent upon the air contained in the 
tube, which will be agitated through its 
whole length, and, by various reflections 
from the side of the tube to the axis, the air 
along the middle part of the tube will be 
greatly condensed, and its momentum pro- 
portionably increased, so that when it comes 
to agitate the air at the orifice of the tube 
AC, its force will be as much greater than 
what it would have been without the tube, 
as the surface of a sphpre, whose radius is 
equal to the length of the tube, is greater 
than the surface of the segment of such a 
sphere whose base is the orifice of the tube. 
For a person speaking at B, without the 
tube, will have the force of his voice spent 
in exciting concentric -superficies of air all 
round the point B ; and when those super- 
ficies or pulses of air are diffused as far as* 
D every way, it is plain the force of the 
voice will there be diffused through the 
whole superficies of a sphere whose radius 
is BD ; but in the trumpet it will be so con- 
fined, that at its exit it will be diffused 
through so much of that spherical surface 
of air as corresponds to the orifice of the 
tube. But since the force is given, its in- 
tensity will be always inversely as the num- 
ber of particles it has to move ; and there- 
fore in the tube it will be to that without, 
as the superficies of such a sphere to the area 
of the large end of the tube nearly. But 
it is obvious, Dr. M. Young observes, that 
the confinement of the voice can have little 
effect in increasing the strength of the 
sound, as this strength depends on the ve- 
locity with which the particles move. Were 
this reasoning conclusive, the voice should 
issue through the smallest possible orifice ; 
cylindrical tubes would be preferable to any 
that increased in diameter ; and the less the 
diameter, the greater would be the effect 
of the instrument; because the plate or 
mass of air to be moved would, in that 
case, be less, and consequently the effect 
of the voice the greater; all which is con- 
tradicted by experience. The cause of the 
increase of sound in these tubes must there- 
fore be derived from some other principles : 
and among these we shall probably find, 
that what the ingenious Kircher has sug- 
gested is the most deserving of our atten- 
tion. He tells us, that “ the augmentation 
of the sound depends on its reflection from 
the tremulous sides of the tube ; which 
reflections, conspiring in propagating the 
pulses in the same direction, must increase 
its intensity.” Newton also seems to have 
considered this as the principal cause, in the 
scholium of Prop. 50, B. II. Princip. when 
he says, We hence see why sounds are 
so much increased in stentorophonic tubes, 
for every reciprocal motion is, in each .re- 
turn, increased by tire generating cause.” 
Farther, when we speak in the open air, 
the effect on the tympanum of a distant au- 
ditor is produced merely by a single pqlse. 
But when we use a tube, all tire pulses pro- 
pagated from the mouth, except those in 
the direction of tiie axis, strike against the 
sides of the tube, and every point of im- 
pulse becoming a new centre, from whence 
the pulses are propagated in all directions, 
a pulse w ill arrive at the ear from each of 
those points. Thus, by the use of a tube, 
a greater number of pulses are propagated 
to the ear, and consequently the sound in- 
creased. The confinement too of the voice 
may have a little effect, though not such 
as is ascribed to it by some ; for the con- 
densed pulses produced by the naked voice 
freely expand every way ; but in tubes, the 
lateral expansion being diminished, the di- 
rect expansion will be increased, and con- 
sequently the velocity of the particles, and 
the intensity of the sound. The substance 
also of the tube has its effect ; for it is found 
by experiment, that the more elastic the 
substance of the tube, and consequently the 
more susceptible it is of these: tremulous 
motions, the stronger is the sound. If the 
tube be laid on any non-elastic substance, 
it deadens the sound, because it prevents 
the vibratory motion of the parts. The 
sound is increased in speaking-trumpets, if 
the tube be suspended in the air; because 
the agitations are then carried on without 
interruption. These tubes should increase 
in diameter from the mouth-piece, because 
the parts vibrating in directions perpendicu- 
lar to the surface will conspire in impelling 
forward the particles of air, and conse- 
quently, by increasing their velocity, will in- 
crease the intensity of the sound : and the 
surface also increasing, the number of points 
of impulse and of new propagation will in- 
crease proportionally. The several causes, 
therefore, of the increase of sound in these 
tubes, Dr. Young concludes to be, 1. The 
diminution of the lateral, and consequently 
