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Theses and Dissertations
1913
The vibration galvanometer, and a test of the
current-sound sensibility of a telephone receiver
Clarence William Hazellett
State University of Iowa
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Hazellett, Clarence William. "The vibration galvanometer, and a test of the current-sound sensibility of a telephone receiver." MS
(Master of Science) thesis, State University of Iowa, 1913.
http://ir.uiowa.edu/etd/3620.
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Hazellett, Clarence William
1913 M.S.
THE VIBRATION GALVANOMETER, AND A TEST
OF THE CURRENT-SOUND SENSIBILITY OF A TELEPHONE
RECEIVER.
The two principal methods
in use for the
measurement of alternating currents depend upo
1
the heating effect produced in a small conductor
carrying the current and the mutual interaction
of two coils operated by currents from the name
circuit, producing a relative displacement which
is proportional to the product of the forces in
the two coils and since they must be of the same
sign, their product must be positive and the
resulting deflection in the same direction.
Both
instruments are thus integrating instruments,
adding up the effect of the current during the
complete cycle.
However neither of these instru­
ments can at all compare in sensibility with
direct current instruments and a sensitive
indicating meter for alternating currents is
much needed in modern research, particularly in
the branches pertaining to telephony.
The ele c tr o­
dynamometer is fairly sensitive but its high self
induction, particularly at high frequencies is a
serious disadvantage.
On the other hand the h o t ­
wire instruments will measure currents of the
frequency of Hertzian waves but is not at all
sensitive to small currents.
It has negligible
self induction and produces no phase displacement
in the circuit, wh i c h is undesirable.
purely qualitative results are desired,
Where
as for
instance in null methods of measuring capacity
and inductance, the telephone receiver has been
used extensively as an indicating instrument.
But on account of the presence of harmonic currents
in the circuit, of high frequency,
to which the
telephone receiver is quite sensitive,
only a
minimum may be determined which destroys the
accuracy of the method.
Here again it is highly
desirable to have an alternating current detector
of high sensibility and moreover one that will
not respond appreciably to any other current than
the fundamental.
The first important step toward the solution
of these problems was made by I'ax 7/ien » in 1891.
His invention was known as the optical telephone
and consisted of a membrane of some magnetic substance
projecting over the magnetic pole of an ordinary
telephone receiver.
A small
mirror was mounted upon
the diaphragm, from which the image of an illumireted
slit was reflected upon a scale.
*Ann. d Physik Vol. 42 p 593
"
"
"
"
44 p 601
It was necessary
that some means be used for producing a current of
the same frequency as the natural frequency of
vibration of the membrane,
or that some method
of varying the latter to suit the former be used.
The first method being much less difficult was
used by Wien.
When such a current is passed thru
the coils wound upon the ends of the receiver
magnet,
a vibration of the membrane is set up
which widens the image of the slit into a band.
It was shown experimentally that the width of the
band for small currents was proportional to the
current.
It will
be seen at once that the essential
principle of this instrument
is the magnification
of small forces by resonance.
The optical telephone
was practically dead beat and could be used for
studying currents which varied quite rapidly with
time, as polarization currents.
With the scale
at a distance of one meter from the mirror,
required 3 X 1 G -7 Amp.
it
to produce one millimeter
deflection or width of band.
In his most sensitive
instrument the diaphragm was replaced by a small
watch spring with a soft iron armature attached to
the end.
This type of construction gave a very
small sensibility to harmonics,
the sensibility
to the fundamental current being at least
hundred times that for the first harmonic.
one
The
range of frequencies of thi3 instrument i3 rather
small
work.
and limits the adaptability to quantitative
It is not at all suitable for hi^h frequency
first on account of the impracticability of
constructing a moving system which will
operate
satisfactorily and have a sensibility of value
and second on account of the high self induction
of such an instrument.
Following out the principle of the
optical telephone
in a somewhat different manner,
Rubens'" designed the first vibration galvanometer
in 1895.
A torsion wire is stretched between two
magnetic ’poles and some small pieces of soft iron
are fastened in a suitable manner* on this wire.
Coils of fine wire are wound about the poles of
i
the magnet and an alternating current in them
producing a differential effect in the magnetization
and providing the moment of inertia of the magnet
system and the free length of the suspension are
properly adjusted the system vibrates in resonance
with the current.
A mirror system is used as in
the optical telephone,
to the wire.
the mirror being shellaced
Systems of various dimensions may be
introduced to get a wide range of frequencies.
This instrument has a sensibility about four times
Q
that of the optical telephone, requiring 7X10
Amp.
per millimeter deflection with the scale at a distance
of one meter.
All instruments of this type, that
is, operating on the principal of resonance have a
very hi~h sensibility just at the resonance point
''Ann. d. Physik Vol.
5G, p 27
while a slight change of frequency of the current
or of the instrument causes a very great decrease
in the sensibility.
sharpnesr
A typical curve showing the
of the resonance of such an instrument
is given in figure 1.
In 1901 Max Wien*improved the Ruben's type
by replacing the soft iron pieces on the suspension
by small permanent magnets.
Instead of using the
differential method however, he uses a field core
built up of small
iron wires to prevent eddy currents
and the coil carrying the current is wound about
this core.
A sensibility was obtained of 1.8X10"8
per mm.
Campbell described in 1907 a vibration
galvanometer constructed on the principle of the
D'Arsonval type.
This instrument has a sensibility
close to the figure given for the instrument above.
It is evidently not adapted for high frequencies
but is very satisfactory for frequencies under 750.
Probably the most important advance in
*Ann.
d. Physik Vol. 309 p. 425
this line of work has been made by Duddell* in the
invention of the bi-filar instrument.
It consists
of an ordinary coil galvanometer reduced to lowest
terms, i.e, a coil of a single turn is placed between
the poles of a very strong magnet and a mirror is
mounted on the same.
A phosphor bronze wire of very
small diameter is stretched over two bridge pieces
between the poles of the magnet and after running
over a tension adjusting device is brought back
parallel to the first part.
When a current traverses
this conductor one part tends to move in one
direction and the other in the opposite direction.
The suspended mirror is thus tilted and under the
condition that the free length of the wires and the
tension is properly
adjusted the system will vibrate
in a manner as described for the other instruments.
A STUDY OF THE VIBRATION GALVANOMETER.
THEORY.
Consider the action of the ordinary galvanometer
in which a relative displacement
is produced by
sending current through a coil situated in a magnetic
field.
If the current is gradually increased to
a maximum the swing gradually increases to its
maximum.
In other words the displacement is in
phase with the force.
If the direction of the
current is reversed at the end of the first swing
the displacement in the other direction will be
greater than the first,
*Phil. Mag. Vol.
and if the direction is
IS, 1909
continuously changed at the proper time, when a
steady state is reached the rate at which energy
is converted is equal to the rate at which energy
is I 0 3 1 by damping, and the maximum displacement
will be much greater than that produced by the first
deflection.
In order that we shall
have the condition
that the motion of the vibrating system shall change
direction with change of direction of the force,
it w.ill be required that the moving system have
the same period of vibration as the impressed
force.
Ordinarily the motion will be simple
harmonic and the restoring force is continually
equal to the displacement multiplied bjr a constant.
However, when a steady state is reached, the
phase of the force and displacement does not
agree as in the above simple case but the moving
system leads the force by ninety degrees.
Rayleigh*
in his discussion of forced vibrations
develops the equation of m o ti o n of such a system.
- •
2
YL-4 kti + n u
E cos pt
where
u is the displacement, k the constant of damping,
n the frequency of the system or the square root of
the moment of inertia divided by the restoring
moment and the right hand expression is the
ordinary term indicating the phase relation.
The solution of this equation is
u = E s ift e c o s (p l + e)
Ep
"Rayleigh's Theory of Sound, Vol.
1, p. 46
where tan e = Rk_
n -o
If n equals p the tangent of the nhase becomes
infinity,
and is therefore n i n e Jy degrees.
Further
if u or aIn zero and since the energy varies as
•
u
2
2
which in turn varies as sin e a solution for
maximum is evidently where the sin e is one.
It is evident from this that when the deflection
passes the zero point that the velocity is greatest
and that the current is a maximum.
Since the
counter electro-motive force develops is a
function of the velocity,
it follows that
the C. E. I'. F and the current are in the same
phase.
the time
The power converted is always equal to
integral of the product of the C. E. M. F.
and the current and it will be at once seen that
a slight lack of timing,
resulting in a phase
displacement of the two will have a marked effect
on the power converted and the sensibilitjr will
thus drop rapidly.
The solution of the equation
expressing the power of any motor containing the
impressed E. I'. F.
and the C. E. M. F.
terms for
a maximum shows that the impressed E. M. F.
should be double the C. E. I'. F.
The fact that
the C. E. M. F. depends upon the strength of the
field makes it possible to tune for maximum
deflection with a given current by varying the
strength of the field or the distance between
nthe poles.
The calculation of the C. E. II. I'.
may be made very conveniently by drawing tangents
to the curve of calibration and the point at which
they cut the E. U. F. axis is the C. E. M F. at that
particular deflection denoted by the point of
t an geney.
A mathematical treatment of the instrument
was reported by Frank V/enner of the U.
S. bureau
of standards in their bulletin of May 1909.
A brief resume' with notes will
If © i s
be given.
the angular displacement°f.<3 Y and
are
constants representing the moments of inertia,
damping,
restoration and displacement respectively,
then from Grey's Abs. H e a s . in E l e c . and Hag. Vol 2,
p. 392 the equation of motio n of the system is
+Q do
o<
&tz
^ x o ~yrL
dt
and the free period is
j_ - z. 77~ ir^ ~
f
The solution of this equation after dropping
terms which disappear when a steady state is
reached is of the following form
Vp73 w T ? "I being the effective value of the current
and determined by the following relation,
- Z " -
^ Co~s cu - f j c o s cr
Y
where Bb is the C. E. M. F.
maximum value of 6.
0 represents the
p 0 and p are the angular velocities of the
displacement vectors of the moving system
and the force respectively.
In the equation
for maximum displacement
small and the
p
p p
quantity (pQ - p ) becomes of great importance
if the two frequencies do not a g r e e ,agreeing
with the observed drop in sensibility under
these conditions as mentioned above.
In the
equation for the effective value of the current
the effective values of the electromotive forces
are obtained simply by multiplying the forces by
the cosine of the angle in order to get the
components which are in phase with the current.
Substitution of suitable expressions for the
current and back E. M. F.
give the following
equations when the instrument is accurately tuned.
V -
w
r(YQ+Vz)
It is seen that the current sensibility is
independent of the moment of inertia and that
it will decrease with rise of frequency.
Moreover the damping is one of the chief factors
in sensibility and should be kept small.
It is
of two kinds, namely electrical and mechanical.
The first can be reduced by eliminating the
possible sources of eddy currents and by
keeping
the proper relations between the impressed and
the back electro-motive forces.
The latter
may be decreased by using the galvanometer in
a vacuum to decrease damping due to air friction
and by employing suspensions of the greatest
elasticity.
It majr be concluded that for use
in null methods it is desirable to use low
frequencies on account of the greater sensibility.
It is of some importance to consider the
sensibility of the instruments to harmonics in
a theoretical manner.
If we substitute in the
general equation for the electro-motive force
sensibility, involving the frequencies of the
force and the system, which is
C.O S CO
0
=
<r
the values of the frequencies of the harmonics for
p we shall obtain the value of 0*for this frequency.
The following result is illustrative of what is
obtained when the smaller terns are neglected,
and considering the ciirrent to have three times
the frequency of the system.
<p3
=
If a definite system of units is adopted and the
sensibilities for the natural frequency and the
harmonic frequency are compared it is found that
the latter is very small compared with the former.
In attempting to increase the sensibility
of the vibration galvanometer by the use of
resonating circuits,
thus getting a magnification
of the electric forces as well as the mechanical
forces by the same principle,
it was noticed that
the connection of an inductance in parallel with
the instrument increased its sensibility.
Suitable
variation of the inductance increased the deflection
for a given current as much as two and one half times.
On the other hand the introduction of any amount
of capacity in the circuit decreased the sensibility
markedly.
I have attempted to explain this on the
ground that the E. M, F. of self induction, being
in quadrature ahead of the impressed E. M. F . ,
which is in quadrature behind the displacement
is thus in exact phase with the displacement
itself and thus should increase the deflection
for a given amount of current.
is however, ninety degrees
E. M. F.
The capacity E. M. F.
behind the impressed
and is hence in direct opposition to
the displacement and should decrease the sensibility.
Wenner has shown theoretically that the use of
self induction should increase the sensibility
under the condition that the impressed frequency
should be raised at the same time.
IIy results
from a large number of trials show that the
sensibility may be greatly increased without the
readjustment of frequency and in each case the
maximum sensibility was reached by increasing the
frequency of the impressed force which agrees with
W e n n e r 1s t heory.
Wenner has also developed the equations
relating the actions of the galvanometer
when
connected to the secondary of a transformer or
when directly connected to the source of current.
The relation of conditions necessary for a maximum
sensibility is derived by solution of the equations
for a maximum.
In some work, using the galvanometer
as a detector in the measurement of the conductivity
of solutions I found it advantageous to use a
transformer but no attempt was madeto get the most
suitable conditions possible.
With reference to the assumptions made in
the theory discussed it should be mentioned that
the moment of inertia may bo considered a constant
only provided that the system is symetrical.
If
it is not symetrical the moments of inertia and
of restoration will change with the frequency.
The moment of displacement will not be exactly
constant since it depends upon the effect
hysteresis and eddy currents,
of
but these are
of small magnitude and it is found the theory
and experiment agree quite closely.
A study of the construction desirable
for laboratory use will disclose a few facts
in
regard to the relative value of the two instruments
in various conditions.
Taking the separate
parts of the instruments for consideration
and discussing the adaptability will be of some
importance.
The construction which will give the
greatest sensibility at hi g h frequency will be
the most sensitive at low frequencies providing
the same system can be used for the low frequency.
In the Ruben's type the strongest magnet for its
weight and one which will have the least air
damping for its cross section is desired.
This requires a compound magnet to be used lor
greatest strength and the distribution of the parts
will be governed by the shape of the field poles,
it being desired that they shall enclose a max i mu m
number of lines of force when placed at right
angles to their position of rest.
Assuming that
the square root of the moment of inertia is
proportional to the reciprocal
of the sensibility
at high frequency and that the damping in air has
the same ratio as the power required to pull an
object of the same shape through a fluid medium
it is easily shown that a rectangular cross section
is to be preferred when the Instrument
is used in
a vacuum while the same general cross-section with
tapering sides is most suitable for work at ordinary
pressures.
In practice it is difficult to mount
such a system,
it being necessary to anneal,
bore, harden and magnetise the metal and it is
found to be quite difficult to get the system
of r.agnets symetrical.
were obtained
magnets.
Not very satisfactory results
in trying to use watch springs for
I!ax ?-rien used a number of small steel
wires fastened upon a small strip of mica, which
was in turn fastened to the suspension by shellac.
The wire used was one of the smallest phosphor
bronze wires obtainable,
but on account
of the fact that the tuning of the instrument
required the clamping of the wire in different
places, which clamping flattened the wire in
such a manner that the zero point shifted
continually with change of free length that
the manipulation of the instrument was very
troublesome.
This serious difficulty might be
remedied by the use of a silk fiber as a suspension
v/hich would be free from this flattening but on
account of its low torsion coefficient would be
useful only at lower frequencies.
The most suitable
size for the mirror is about 2-3 m m square.
If made
larger the period of vibration is too great and if
too small the image of the slit is poor due to
diffraction.
The most satisfactory mirrors were
made by blowing small glass bulbs which were very
irregular in shape, silvering them on the outside,
breaking them up into small pieces ana selecting
cl
pieces having a radius of curvature suitable for
the scale distance.
The field, core should be
laminated to prevent the formation of eddy currents
and there should be no collars or large pieces of
metal about the pole tips on account of the
transformer action which may impair the efficiency
greatly.
It should be possible to vary the distance
of the magnetic poles from the m o vi n g system as this
"ives an easy method of the most accurate tuning
and this adjustment should be micrometric.
If the
instrument is to be used in avacuum it has been
found advisable to do the final tuning by means of
a magnetic shunt operated outside of the vacuum
chamber.
The tuning is quite sensitive to this
and the change of damping is seen to explain the
action,
in the same manner as the variation of
the field of an electric motor changes the speed.
The coil for the field should preferably be divided
into separate coils which can bo connected in
series or in parallel.
A coil of four ports
having a resistance of fifty ohms each was used,
#36 wire being used.
The metho d of calibration
used was to connect in series with a battery
an electronagnetically operated
was tuned to the galvanometer,
interrupter, which
in series with
these were the galvanometer and a large non-inductive
resistance,
the galvanometer being shunted also at
times.
The effective value of the E. M. P. across
the galvanometer and the series resistance was
deternined and the circuit was considered as being
without self induction, which is not very great
at the frequencies used.
No quantitative results
connecting frequency and sensibility were sought
but it was simply noticed that the sensibility decreases
with increase of frequency.
A calibration of the
»■
instrument at a frequency of 100 is given below
by the curve Fig.
2. Theoretically it appears that
the curve should not be quite so straight on
account of the increase of C. E. I,'. F. with
increasing deflection.
The sensibility of this instrument was not as high
as that obtained by 7/ien, the current required to
O
give one m m deflection being 6.9 x 10-
If a conductor is stretched in a magnetic field
and a current passes through it the wire tends to
move in a direction at right angles to the current
and the field.
If the same wire is returned through
the same field, the relative direction of the current
is opposite and the displacement is opposite,
so
that a mirror fastened upon both of them will be
tilted.
If the free length of the wires and their
tension are capable of adjustment we have a variable
frequency,
vibration galvanometer.
The wires are
made of the smallest phosphor bronze material
obtainable,
i.e.,
.0015 in. in diameter and the
variation of their free length is effected by two
sliding bridge pieces in which they rest.
The c o n ­
struction of the mirror is the same as that with
the other type 7/ith the additional precaution
that the rear of the mirror should have a coat of
paraffin to prevent the conducting layer of silver
from short circuiting the two conductors.
In some
cases it is desirable to have the resistance of the
instrument as low as possible and a suggestion may
not be out of place.
The upper bridge piece should
be conducting thus cutting off the resistance of
the upper ends which are not in use and the lower
bridge being necessarily insulating m a y have two
conducting pins connected with low resistance
flexible conductors to remove the resistance of
the lower part not
in use.
The magnetic field
should be the strongest available and the magnetic
pole faces should be narrow rectangles
in cross-
section, having their long side parallel to the
suspension and as close to it as possible.
A
spring is found necessary between the j-ing over
which the suspension runs and the tension a d ju st ­
ing screw in order to prevent breakages.
The general theory given applies to this instrument
as w e -11 as to the instrument previously described.
The accompanying diagrams will give a general idea
of their construction.
The source of current used in the
calibration of the instruments was an electromagneticallv operated
either of
inter axpter consisting
a tuning fork
or vibrating wire.
Two insulated contact devices were necessary
one for the operating current and the other for
the testing current.
Contact was nade by
means of small platinum wires dipping into
mercury cups the contact being shunted by
condensers to prevent sparking.
The vibrating
wire possesses the advantage that it can be
tuned to a wide
range of frequency. A rather
large iron wire has two short sharp pointed
platinum wires soldered to it.
A large wire
is needed for a small wire heats when the current
ir sent through it necessary to operate,
thus
THE SINGLE SUSPENSION VIBRATION GALVANOMETER.
W i s t h e wedge u s e d f o r v a r y i n h f r e o l e n g t h o f w ire
b u t g e n e r a l l y some c l a m p i n g d e v i c e is u s 3 d . I P s t h e
m i r r o r , S t h e magnet s y s te m and F t h e f i e l d .
BI-FILAR VIBRATION GALVANOMETER.
M is the mirror
W
the wedges
S the spring
changing the elasticity and hence the pitch.
It
is not possible as night be expected to have a
piece of soft iron attached to the center of the
wire to get a greater magnetic effect on account
of the consequent damping of the fundamental.
In an instrument of the single suspension type
it is found that the interrupter must be at
considerable distance from the galvanometer for
obviously the galvanometer is very sensitive to
changes in magnetization which are tuned to it.
Where available a generator of constant speed
but variable would be most desirable, while
a motor generator set operated in synchronism
with a tuning fork would give the greatest accuracy.
For null methods a tuning fork interrupter is
found to be very satisfactory but only suffices
for qualitative work.
To eliminate the effect of
harmonics hi#i frequencies s’
n ould be used while
for the greatest sensibilities low frequencies are
bet ter
The methods of tuning, part of which have
been suggested are as follows:
suspension and the bi-filar,
For the single
the variation of
the free length of the suspension, the moment of
inertia of the moving system, the distance of the
pole faces from the moving system and the use of
the mngnetic shunt are all found to be favorable
under certain conditions.
Wi t h the bi-filar a
variation of the tension gives the fine adjustment
in tuning.
A stroboscope method of tuning was
devised for accurate tuning and to indicate whether
the instrument was responding to harmonics or the
fundamental.
It consisted of a mirror mounted
on the shaft of a constant speed D. C. motor
and so fastened that its plane was not perpendicular
to the axis of the motor.
The intermittent light
produced at the interrupter when view reflected from
this rotating mirror appeared as a ring of sparks
which remained stationary if the speed of the motor
was an aliquot part of the frequency of the interrupter
If a small mirror was placed at the zero point of
the scale of the galvanometer so as to reflect the
image of the slit upon the rotating nirror also,
when the nirror was vibrating just twice as many
images of the slit are reflected from the rotating
mirror as from the interrupter and if one set of
images stands still the other will also if
properly tuned.
Any other ratio than two to one
indicates a response to an incorrect frequency.
Where a generator is used instead of the interrupter
an incandescent lamp having a gas immersed filament
will give the stroboscopic effect and in this case
t iere will, be an equal number of images of the slit
and the light.
Since our aim is to be able to
use the galvanometer as a quantitative instrument
very accurate tuning is necessary and the very
sharp resonance curve makes it imperative.
lack of tuning does not throw
A slight
the system out of
step but causes it to make forced vibrations
which lag in phase behind the current.
It may be
mentioned that the above described stroboscope
has a number of quite importan possibilities in
demonstration of intermittent light phenomena
and as a practical device in several branches
of alternating current work.
An experimental comparison of the two
instruments shows that all most all differences
of the two types is in favor of the bi-filar.
The
bi-filar may be tuned by making the rough and fine
adjustments while looking at the scale while with
the other type a trial adjustment must be made and
then observed, making the process very tedious and
uns a tisfactory.
The shifting of the zero point
as before mentioned does not occur at all with the
bi-filar.
The bi-filar is more easily operated
in a vacuum due to the greater ease of tuning by
varying the current in the field.
The bi-filar
has the lowest resistance, the least self induction
possible,
sharper resonance, no eddy current losa
to mention, higher sensibility, easier manufacture
and insertion of suspensions, and possessing a
much greater range of frequencies.
As pointed
out, the max im u m power converted occurs when
the impressed E. M. F.
is double the C. E. M. F.
There is no method of calculating the C. E. M. v .
for the single suspension but the following
simple equation will give the C. E. M. F.
for
any deflection.
E, - 2 D* sin*x* A* (D*P
b
TUB---------where E b is the C. E. M. F . , A is the free
length of the wires, P is the frequency, fl) the
flux density, D the distance between the two
wires of tht
suspension, x is the angular deflection
of the mirror or
x - t a n -1- R
where R is one half the total width of the band
image of slit, and L the distance from the scale
to the mirror.
In the results to be given in the
latter part of this paper it appears that the
bi-filar instrument may be used satisfactorily
for quantitative work and that it may be
depended upon to give consistent results.
*
Moreover I have used the vibration galvanometer
as a detector in the measxirement of the
conductivity of solutions by the Kohlrausch
bridge method and the results obtained
are incomparably more accurate and consistent
than the older methods.
It seems probable that
the vibration galvanometer, when tuned to the
frequency of the trains of waves striking the
antennae of a wireless telegraph system, might
be used in place of the telephone receiver
when it is used with the crystal rectifiers or
the Marconi detector.
Since the vibration
galvanometer will detect a current one hundred
times as small as that required to produce an
audible sound and since its time constant is
small it would possibly be of value
in this field.
TIP CURRENT-SOUND SENSIBILITY OF THE TELEPHONE
RECEIVER.
In the study of architectural acoustics
some method of measuring accurately the intensity
of sound at various parts of auditoriums,
is greatly to be desired.
etc.,
Three principal methods
have been used in measuring the absolute intensity
of sound, namely;
by means of the Rayleigh disc,
by measuring the increase of pressure at reflecting
surfaces by means of a balance,'"'and by the change
of pressure at the nodes of stationary waves
being measured, using a manometer* Still
another
method using optical interference hrs been u s e d / ’
As a combined test of the use of the vibration
galvanometer for quantitative use and a search for
an easier method of measuring the current-sound
sensibility of the telephone receiver, we have
devised a method in which a source of sound of
variable
intensity sets up vibrations which impinge
upon the diaphragm of a telephone receiver and
act upon a Rayleigh disc.
The current generated
in the telephone receiver is measured by means of
the vibration galvanometer connected, directly thereto,
while the absolute sound intensity is determined
* Zernov. Ann. d. Physik, 26,
1908, p. 79.
* Altberg,
"
"
"
11,
1903, p. 405
* Raps,
"
"
"
36,
1889, p. 273
*
11
"
"
50,
1893, p. 193
"
from the deflection of the Rayleigh disc.
The constant source of sound intensity
consisted of an electromagnetically operated
tuning fork mounted upon a resonator and actuated,
by a current which was variable and thus varied
the intensity of sound without varying the
frequency of the note appreciably.
A second method
of varying the intensity was used to insure against
the possibility of the variation made in one
m a n n e r ,distorting the results.
The two curves
were identical within the limit of experimental
error.
A diagram of the apparatus is given below.
A is the telephone receiver and the resonating
tube connected therewith, B is the tuning fork
apparatus and G represents the vibration galvanometer,
and D is the Rayleigh disc apparatus.
requires some description.
This part
A brass tube was originally
used having a length equal to the half wave
length
of the sound used.
One end is closed by means of
a telescoping brass tube so as to be able to tune
the instrument accurately, the other being very
tightly closed by means
of a diaphragm.
Over this
end another tube is placed which has a length
of a quarter wave, for the purpose of obtaining
resonance in order to get a larger change of pressure
at the node.
A light silvered disc is suspended
in the eenter of the longer tube and the change
of pressure at this point produces a constant
deflection which has been shown to be directly
proportional
to the incident sound intensity.
An ordinary mirror and scale is used to read the
deflections of the disc.
Dr.
Stewart has modified
this and obtained a greater sensibility by
narrowing the tube down to a small channel in the
center, thus virtually concentrating the pressure.
The work of Stewart and Stiles
■Sfr
indicate that
the deflection is proportional to the sound intensity
outside of the tubesnd it seems allowable to assume
the
same relation to hold in this case.
Some
precautions of manipulation must be observed.
The relative positions of the instruments must not
bechanged or of other objects in the room on
account of the fact that we have standing waves
i n the room and inconsistent results must follow.
Even the movement of the hands of the observer
will distort results and it is neccesr.ary that
he must be able to read both galvanometer and
Physical Rev.
April 1913
Rayleigh disc apparatus without moving the head.
In order to have the intensity of sound to remain
constant with given conditions
have
it is necessary to
a very smoothly operating contact device,
and
a spring upon a spring was employed, made simply of
platinum wire and fastened directly to the fork.
The other method besides that of varying the current
in the operating coil to change the sound intensity
was to slide a disc covered with felt across the
opening in the resonator box.
In the curves
given the points marked by o were made by this
latter method.
The calibration of the galvanometer
is that given in the first part of this paper and it
will be remembered that it is a straight line over
the range used.
The indications of both instruments
wi]] not be over three or four per ccnt in error.
The resulting curves taken under the best
conditions are given on the next page.
It is to
be noticed that they are approximately parabolic
and the more distant points on the
curve approach
a maximum for the amount of current.
of the current,
The square
that is, a constant times the e nergv
when plotted with the sound intensity gives approximately
a straight
line, indicating that the two energies
are proportional.
The receiver used is thus
calibrated and given the same conditions with any
intensity of sound and a particular point of the
curve is determined or vice versa.
The frequency
used was 256 and it w o ul d be much better to use
a frequency corresponding to the natural frequency
of the telephone receiver, which ordinarily is
near 700.
A typical sensibility curve of a telephone
is given below where the frequency is varied,
and it
will be seen that for resonance the sensibility is
much greater.
The least audible current is plotted
with frequency in this diagram.
A tentative theory which may account for
the results obtained may be made if we are allowed
to assume that the amplitude of vibration of the
vibrating diaphragm is directly proportional to
the change in pressure
or the
condensation.
It
seems reasonable that this should be the case
at least with small amplitudes.
If we call the
displacement X and assume S. II. motion, then X
varies as the
amplitude.
Now the E. M. P.
generated
in the receiver is proportional to the current in the
circuit,
if we can neglect the self induction, and
it is obviously proportional to X.
Since theory shows
that sound intensity varies as the square of the
condensation, hence, the current should vary as
the square root of the sound intensity, or Should
give a parabola when plotted,
and moreover,
the
square of the current should vary directly with
the sound intensity.
This rather crude theory
agrees with e x p e ri me nt a l■results accurately
but it is to be admitted that several other
conditions are to be taken into account.
Several
receivers should be studied to see if the
relation continually holds.
Since resonating
instruments have in general greater sensibility
it would be somewhat important to design a
receiver having a low natural frequency for this
purpose, and having a large diaphragm and wide
magnetic poles in order to be quite sensitive.
It may be suggested that the telephone receivers
used in wireless telegraphy with rectifiers be
tuned as nearly as possible to the train frequency
of the incoming waves,
since a much higher sensibility
may be obtained as is shown by the curve given on the
previous page.