[From the American Journal of Science and Arts, Yol. IY, Nov., 1872.J 
ON A METHOD OF DETECTING THE PHASES OF 
VIBRATION IN THE AIR SURROUNDING 
A SOUNDING BODY ; 
AND THEREBY MEASURING DIRECTLY IN THE VIBRATING AIR 
THE LENGTH OF ITS WAVE AND EXPLORING THE 
FORM OF ITS WAVE-SURFACE. 
Professor of Physics in the Stevens Institute of Technology) [ o b o k e n, N. J. 
By ALFRED M. A] AYER. Ph D.. [From the American Journal of Science and Arts, Vol. IY, Nov., 1872.] 
ON A METHOD OF DETECTING- THE PHASES OF 
VIBRATION IN THE AIR SURROUNDING A 
SOUNDING BODY; AND THEREBY MEAS- 
URING DIRECTLY IN THE VIBRATING 
AIR THE LENGTH OF ITS WAVES 
AND EXPLORING THE FORM 
OF ITS WAVE-SURFACE. 
By ALFRED M. MAYER, Ph.D., 
Professor of Physics in the Stevens Institute of Technology, Hohoken, N. J. 
The curve A, B2, B4, etc., is the well known symbolic repre- 
sentation of the dynamic condition of the air, at a given instant, 
when traversed by simple sonorous vibrations. Those portions 
of the curve above the axis OX represent the length and manner 
A 
B1 
B2 
B3 
B4 
B5 
B6 
o: 
;X 
of the aerial condensations, while those flexures below the axis 
represent the rarefactions; therefore similar points of the flex- 
ures above the axis, or similar points in the flexures below the 
axis, represent like phases of vibratory motion. Imagine these 
conditions of the air produced by a body vibrating at A; then 
the distance A to B1, B1 to B2, etc., will equal a half wave-length, 
while from A to B2, B2 to B4, etc., will represent a whole wave- 
length, corresponding to the note given by A. If another 
sonorous body B, giving exactly the same note as A, be placed 
anywhere on OX, it will have vibrations communicated to it 
from the vibrating air which touches it, and it will vibrate 
exactly with the air, almost as though its substance was of the 
air itself. Now imagine this body B placed at B2, or at B4, or 
B6, etc., then its phases of vibration will be exactly similar to 
those of A; but when placed at B', B3 or B5, etc., its phases 
of vibration will be opposed to those of A. That is, at dis- 2 
tances from A, equal to any number of whole wave-lengths the 
body B will, at the same moment of time, swing with A, but 
at distances from A equal to any number of half wave-lengths 
the direction of its swings, at any given instant, will be opposed 
to A; while at intermediate positions, on the line OX, the 
oscillations of B will be lagging somewhat behind or be slightly 
in advance of the phase of A’s vibration. 
After this it is evident that if, by any means, we can see at 
the same time the vibrations of A and of B, we will (if the 
received conception of the nature of a vibration’s propagation 
is correct) see their motions just as has been described above, 
and will therefore be able to measure, directly in the air, a wave- 
length and to determine any wave surface enclosing a vibrating 
body. I have devised several processes. I will, however, here 
describe only two; the first, though impracticable, I speak of 
to render clear the general method of all; the second I give on 
account of its simplicity, ease of execution, and the superior 
accuracy of its numerical results. 
Take two tuning forks giving the same note and having 
mirrors attached to their similar prongs ; place one at A, the 
other anywhere on the line OX. Keflect a pencil of light from 
each mirror of the forks to a revolving mirror, whose axis of 
rotation is in a plane parallel to the planes of vibration of the 
forks. If the fork B, which vibrates sympathetically, be 
placed at B2, B4, B6, etc, then the two pencils reflected from 
the forks will, on striking the revolving mirror, be drawn into 
two sinuous curves, and the flexures of the two curves will 
run parallel to each other, that is, the curves will appear as 
the two rails of a sinuous railway; but, if the fork B be placed 
at B', B3, or B5, etc., then the sinuosities of the two curves 
will no longer be parallel but will be opposed; that is, where 
a flexure of one of the curves is concave on the left, the 
opposite flexure of the other curve will have its concavity 
on the right. If the fork B be placed at intermediate positions, 
in reference to those above stated, we will have neither concord- 
ance nor opposition of the flexures, but intermediate relations 
depending on the fraction of half wave-lengths at which the 
sympathetic fork is placed on the line OX. 
It is now readily seen that if we should place the fork B at 
two successive points, as B2 and B4, on the line OX, so that 
exact concordance of flexures of the curves should be seen at 
each of these points, then evidently we have placed the fork at 
two positions removed from each other by -a wave-length, for at 
these points the air had at the same instant the same phase of 
vibration. Thus we have measured a wave-length. Further- 
more, if by any means we could move the fork B around A 
so that during this motion it always preserved, in reference to 3 
A, the same relation of vibratory phase, we would have deter- 
mined the form of the wave-surface produced by the propaga- 
tion of A’s vibrations. 
The above is an exposition of the thoughts that have occu- 
pied my mind for several months, and they ultimately led to the 
following method, by which all I have narrated can be accom- 
plished without any difficulty ; thanks to the inventive genius 
of Mr. Konig, to whose skillful aid so many physicists are con- 
tinually indebted. 
The membranes of Mr. Konig’s manometric capsules furnish 
us with surfaces which vibrate in perfect accordance with the 
air which touches them, and we can lead the impulses of these 
membranes through gum tubes to gas jets placed at any desired 
point, where the vibrations of their flames can be compared. 
Thus they are far superior to the tuning forks, which require 
the relations of delicate adjustments to be maintained during 
each change of position, and therefore forks could only with 
difficulty be made to serve in the measure of a wave-length, 
and could not at all be employed to trace out a wave-surface 
on account of the impossibility of a continuous comparison of 
their vibrations, which latter condition the manometric flames 
admirably fulfill. 
Let ns now proceed to experiment. I placed on the acoustic 
bellows an open UT3 organ pipe, and from its ventral mano- 
metric capsule I led a tube to a gas jet placed in front of a 
cubical revolving mirror. I took an UT8 Iielmholtz resonator 
and adapted to its beak a gum tube, with an interior diameter 
of 1 centimeter and a length of over 4 meters. This tube led 
to a firmly supported manometric capsule whose flame was 
placed quite close to and directly behind, the organ pipe 
flame, which latter had about twice the height of the resonator 
flame. On sounding the pipe and holding the resonator quite 
near it, the two flames, by a slight adjustment, were made to 
appear as one series of serrations in the revolving mirror. Now 
on gradually moving the resonator away from the pipe, I saw 
another series of serrations (those of the resonator flame) slowly 
evolve themselves from the first series, and gradually slide 
over the latter, until, having removed the resonator from its 
first position by about H6 centimeters or a half wave-length 
(German), I had the pleasure of seeing the series of moving 
serrations standing exactly midway between the first or im- 
movable series. On moving the resonator yet farther from 
the sounding pipe, I saw the serrations of the resonator flame 
continue their onward progress until the two series again coin- 
cided ; and on measuring the distance of the resonator from its 
first position near the pipe, I found it to be equal to a whole 
The Experiments. 4 
wave-length of the note UT3. When I had removed the re- 
sonator one and a half wave-length, I again saw the serrations 
of the resonator flame bisecting the spaces between the serra- 
tions given by the organ pipe flame, and when the resonator 
had progressed from the pipe to a distance equal to two whole 
wave-lengths I saw that the serrations of its flame had pro- 
gressed to another coincidence with those of the organ pipe; 
and so on, until I had determined on the line of the resona- 
tor’s motion all the phases of vibration corresponding to three 
whole wave-lengths. I now moved the resonator until I had 
again caused the serrations of its flame neatly to bisect the 
spaces between the serrations of the organ pipe flame, and mov- 
ing around the organ pipe, with the resonator held at such 
distances from it that the bisections were steadily kept, I de- 
scribed in space the wave surface of the sounding pipe. This 
surface I found approximately to be an ellipsoid with its foci 
at the top and bottom of the pipe. Nothing could be more 
satisfactory, and it was charming to behold how neatly the 
surface could be determined ; for a small change in the distance 
of the resonator from the pipe produced a sensible shifting of 
the serrations. I now substituted for the resonator an organ 
pipe, in every respect similar to the one on the bellows, and 
with it I repeated the wave-length measures previously made 
with the resonator ; indeed the column of air in the pipe in 
my hand responded so perfectly to the sounding pipe that I 
thought it gave more marked results than those produced with 
The manometric flame-micrometer. 
In the experiments described above, we examined the appear- 
ances in the mirror with the unaided eye, and with it estimated 
when coincidences and bisections occurred ; but to obtain results 
of precision, a method was devised which determines neatly 
these critical points. For that purpose I have invented the 
following micrometer, founded on a beautiful suggestion of 
Dr. R Radau, who thus describes in his excellent “ VAcoustique ” 
(Paris, 1867, p. 272), a method of observing the flames of two 
similar sounding organ pipes. “We attach to the two pipes 
two of Konig’s flames arranged so that the point of one flame 
reaches above a small fixed mirror which hides its base, but 
which shows by reflection the base of the other flame. This 
produces the illusion of a single flame. If now we observe 
this hybrid image in the revolving mirror while we sound the 
two pipes, the point separates from the base, which proves that 
the two flames shine alternately, and the one retracts while the 
other elongates; if the two tubes acton the same flame, the 
effect is null, and the flame remains immovable.” By placing 
the above “ small fixed mirror ” on a divided circle; or by 5 
silvering its back and determining its angular displacements 
around a vertical axis by the method of Poggendorff,—that is, 
by observing through a telescope, the reflections of a fixed scale 
from the back of the mirror,—we have devised a simple and 
precise micrometer for ascertaining the amount of displacement 
of the resonator’s flame. For, having once determined, for a 
given note, the amount of angular motion of the mirror required 
to move the bases of the flames over the distance between the 
centers of two contiguous serrations we have the angular value 
of a displacement equal to that caused by moving the resona- 
tor through a wave-length, and a fraction of the turn required 
to produce the above movement of the bases of the flames will 
be equal to that produced by the remove of the resonator 
over a corresponding fraction of a wave-length. Thus can be 
measured very small fractions of a wave-length. Indeed, even 
with the unaided eye and without the use of the micrometric 
mirror I have distinctly detected a displacement of the flames 
on moving the resonator, (UT3) over only 3 centimeters or pTth 
of a wave-length, and with the micrometer I feel assured that 
I can determine the wave-surface of a body giving the note 
UT 3 to one centimeter of its true position. Of course with 
higher notes we shall get a proportionally closer determination. 
But the object of this paper is not to present numerical results ; 
I reserve these for a subsequent communication, in which I will 
also present diagrams of apparatus and the appearances of the 
flames in various experiments. 
I will here remark that the success of the experiments de- 
pends on the resonator with its attached tube being in perfect 
unison with the organ pipe; also, the relative heights and posi- 
tions of the flames should be so adjusted that the sharpest 
definitions are obtained in the rotating mirror, and thus be able 
to detect and measure the effects of small changes in the position 
of the resonator ; but these and other manipulative details will 
readily occur to any physicist who repeats the experiments. 
Applications of the Method. 
When the method I have here blocked out shall have been 
reduced to the refinement which it is susceptible of, I feel con- 
fident that we will have in onr hands the power to attack many 
problems of high theoretic interest which have heretofore been 
deemed beyond the reach of experiment. Its application to 
such are so numerous that they are almost co-extensive with 
the phenomena of sound. 
The actual experimental determination of wave-surfaces in 
free air and in buildings can now certainly be accomplished ; 
and such determinations may serve to extend our knowledge in 
the direction of giving the proper laws which should govern 6 
architects in their construction of rooms for public assemblies. 
The differences, if any, in the velocities of sound, corre- 
sponding to vibrations differing in intensities and frequencies, 
may be determined by the use of reflectors, and the direct 
observation on any changes in wave-lengths different from those 
which should be given on the assumption that notes of various 
intensities and heights are propagated with the same velocity. 
We can determine a wave-length quite accurately by the 
following arrangement of apparatus. Take an organ pipe with 
a resonator in unison with it, and place the resonator in a fixed 
position opposite the mouth of the pipe, then lead tubes 
from the capsules of pipe and resonator to contiguous jets, and 
adjust their flames to coincidence or to bisection of serrations; 
using for this purpose the manometric micrometer. Now sup- 
pose, for simplicity, that the pipe gives 340 complete vibrations 
in a second; then, as the velocity of sound is 340 meters per 
second, it is evident that in ? °f a second an aerial pulse 
will traverse one meter. Therefore, if all things else remain the 
same, and we lengthen the resonator tube \ meter, the serrated 
flames of the resonator will be displaced | of the distance be- 
tween the centers of two contiguous serrations; and if the tube 
be lengthened 1 meter, or one wave-length, the displacement will 
amount to the entire distance separating the centers of two 
contiguous serrations: and for n number of wave-lengths of 
elongation of tube, we shall have n number of such displace- 
ments. Thus can be measured a wave-length; and if the 
number of vibrations given by the pipe be accurately known, 
we can reach with the manometric micrometer an accurate 
determination of the velocity of sound. 
Finally, we are bold enough to believe that we have in the 
highest development of the method, a means of tracking in 
the air the resultant wave-surface of combined notes ; and, in 
short, of bringing the exploration of acoustic space to approach 
somewhat to that precision of measurement which, for over 
half a century, has characterized the study of the sethereal 
vibrations producing light. 
September 21st, 1872.