The Phenomenon of Resonance
Source: Guilford College
Contributed by: Wood, J. Densmore
Stable URL: https://www.jstor.org/stable/community.17191186
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SENIOR
J.
g
THESIS
Densmore
Class
Wood
of 1915
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4
TEER
THE
PHENOMENON
#
&
There
were
separate
for
and
instance,
great
deal
were
each
not,
however,
never
dreamed
the
explanation
Heat,
and
were
of
such
of
motion
things
as
bits
of
sound,
the
of
air
light
of
well
physies
of
data
and
a nunber
among
of
phenomenon
fairly
interrelation
a mode
the
smattering
understood
as
sub-divisions
Around
gathered
any
explained
when
superstition.
their
RESONANCE
Ž
distinct.
were
more
EH
a time
partially
mental:
to
was
wes
OF
light,
and
a
eleetrieity
the
laws
funda-
know.
There
branches,
Sound
by
Aristotle
waves
or
but
was
he
electromagnetice
waves,
The
connecting
see
to
this
take
tion
by
wave
link
theories
between
connection
each
of
the
of
simple
projection
of
harmonic
a point
motion,
it
and
kinds
a simple
moving
in
and
sub-divisions
resonance
different
has
stepped
interrelation
like
Resonance
ation
these
and
a phenomenon
have
of
of
is
to
in
as
uniformly
the
in
To
necessary
notice
waves
the
physics.
only
explanation
such
formed
its
produce-
turn.
in
the
motion
a circle
considerof
the
upon
&
diameter.
Consiãer
(Fig.
l1).
Let
it
the
be
point
required
P moving
to
get
in
an
a circle
of
expression
motion
of
its
on the
diameter
radius
for
the
projection
AOC.
r
up-
This
will be the motion of the
point
B.
Let
plete
`
Fig.
the
revolution
1
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time
of
of
com-
P
around
ape
the
circle
be
or t/f part
of
Then
2
But
-2T
point
8
Then
X=Y
If
begin
we
x=
=- œt
have
the
and
Æ =
motions
same
to
P
=
loc
O0OB=%
time
the
after
the
expression
particle
resehes
becomes:
the
considered.
period
we
difference
If we
can
assume
consider
two
of
phase
that
the
cases;
between
two
&
/
motions
Æ
O
the
first
case,
to
the
the
particles
two
displacements
at
moving
along
circular
motions
do
the
time
seme
and
the
not
the
get
re-
is always less than the sum of the displacements of
separate
motions.
By
plotting
absissas
represent
nates
A- to
+)
represents
maximum
c
from
= LEOA.
to
of
count
of at A,
corresponding
the
moves
cev. œT
diameter
sultant
point
0
In
their
the
Bard at
r csv (œt
£ here
two
see.
a
Then
ahou
the
t
8> ATE
E instead
apa
in
a revolution.
Then
-l
some
T.
is
of
the
motions
the
two
equal
at
a and
displacement:
may
motions
any
time
be
ordinates
represented
and
to
as
e
the
the
by
Fig.
resultant.
algebraic
b.
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sum
and
time
2.
a
The
oräinate
of
the
and
as
b
ordi-
J
agm
other
each
the
to
aecording
Fig.
3.
Fig.
3
with
coinciães
x-axis.
In
their
to
get
resultant
is
case
the
maximum
E
when
different
when
E
the
is
and
the
the
sum
of
case
may
be
represented
this
amplitudes
zero
anå
so
that
represented
they
not
would
combine
to
a and
with
coincide.
a maximum
give
b
in resonance
a and b, are said to be
they
4.
Fig.
by
the
4
I have
figure
to
equal
always
value
resultant.
When
reach
instantaneously
is
This
partieles
the
zero
to
It
two motions,
These
equal
displacements
Fig.
In
is
a maximum.
motions,
two
of
resultant
The
destroy
even
the motions
180
E is equal to
When
the
their maximum value
intervals.
In the
are
periods
same
not
the
same
simultaneously
way
we may
only
represent
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the
|
motions
at
this
infrequent
case
by
Fig.
5.
Fig.
The
equations
representing
K=
and
the
angular
The
resultant
maximum.
in
motions
in
the
this
same
the
have
when
due
in
motion
and
same
direction
the
Eere
and
we
the
pull
pull
swing
the
on
with
motions
difference
not
will
in
curve
be:
period.
and
not
a
occur.
for
resonance
and
the
will
is
second
that
is
the
that
two
they
be
the
so
be
is
right
If
that
are
a string
given
swing
the
time
and
we
the
greatly
ps
by
pendulum
motion
the
resonance
by
it
numerous.
will
the
If
vibrate
equation
art%
of
the
of
of
a period
=
it
as
resultant
aia
two
irregular
does
suspended
attraction.
motion
at
the
an
examples
length
earth's
ball
of
is
the
phase.
1l equals
to
with
period,
T
where
wt
case
same
a small ball
set
ew
requisite
Mechanical
we
wt
therefore,
first
have
tw
varying
Resonance,
The
Y
KET
velocity
5
of
attach
the
and
of
for
of
swinging
increased
with
the
pull
motion
the
right
S
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acceleration
another
direction
increased
and
g equals
of
the
string
pull
ball
is
the
very
in
the
ball.
length
the
in the
amplitude
little
are
to
effort.
resonance
of
Unless
time
ape
the
motion
resonance
is
of
impaired
the
two
Again
or
even
we
suspend
different
lengths,
as
l,
and
suspend
three
we
we
can
easily
due
to
a
laek
of
motions.
if
if
destroyed
2,
and
light
illustrate
X
three
3
heavy
in
weight
resonance
balls
Fig.
6,
balls
and
SSSSSISIESSEEKÁIS STEEF
by
from
from
also
strings
a wire
the
lack
same
of
of
AB,
wire
resonance.
TEESLISIELEESETFI TEESCESE
|
i
|
©
.
O
URIZ
Fig.
Make
the
lengths
of
since
the
it
independent
is
having
the
l
periodsof
same
When
and
the
of
any
6
4,
2and
simple
one
will
of
the
5,
and
3
pendulums
the masses
length
ZZZZIT
also
of
the
have
and
are
ball
the
pendulums
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is
6
equal.
given
and
same
set
Then
by
those
pendulums
period.
in
motion
the
-6-
resonance .
or
,
5,
and
will
vibrate
in
resonance.
l,
that
they
the
motion
The
motion
the
same
at
stepping
for
his
fall
with
the
motion
plot
a sine
curve,
ferent
tone,
by
resonancè
of
Examples
glass
have
windows
resonance
with
If
two
powerful
you
stand
are
b
which
will
time
and
rise
of
in
known
to
be
may
motions
by
sound
break
absissas
two
sounds
and
sounds
two
the
as
lengths,
wave
are
due
may
dif-
be
a
certain
point
just
4.
Great
numerous.,
to vibration
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in
rep-
the
e
in
organs.
at
we
get
we
of
represented
Fig.
If
manner.
similar
time
and
sounds
resonance
been
water
combining
harmonic
of
so
may
different
two
of
break
resonance.
water
a very
in
the
of
a and
5.
Fig.
a
body.
having
Resonance
resultant.
like
is
the
ordinates
as
case
The
that
his
combine
amplitudes
their
resented
of
waves
Sound
in
waves
produce
to
as
steps
bridge
of
a bucket
carrying
in
person
A
in
be
not
must
steps
These
safety.
are
therefore
must
They
dom.
it
break
the
to
give
to
they
when
soldier
each
add
woulà
time
might
which
vibration
step
to
by
bridge
the
given
a bridge,
crossing
army
an
of
that
is
example
third
A
pendulum.
e neighboring
of
by
affected
be
will
they
before
resonance
in
vibrate
necessary
is
it
pendulums
these
In
respectively.
3
and
2,
with
correspond
will
motion
Their
it
which
with
motion
the
out
pick
6 will
4,
pendulums
the
of
each
and
awkwardly
wobble
will
wire
the
consecutively
instant
same
the
at
motion
in
set
all
are
3
anå
l,2,
If
in
are
phase
and
period
same
the
having
motions
These
quiet.
remain
will
others
The
period.
same
the
of
motion
up
take
will
period
same
the
consequently
and
length
same
the
has
that
one
the
old
senate
=P
chamber
is
at
Washington,
the
deal
louder
than
faet
that
a great
due
to
the
the
dome
lower
witk
and
come
cheəmber.
an
out
increased
is
the
mouth
altered,
out
of
the
waves
fork
voice
voice.
in
from
This,
waves are
the
giving
with
the
dome
I suppose,
reflected
resonance
unite
may
be
a tube.
length
tube
sound
your
the
effect
is
about
in
waves
in
of
the
a wave
amplitude.
of
the
of
your
nearly
These
A tuning
over
the
echo
in
set
Then
may
be
resonance
into
if
the
found
with
vibration
length
where
the
of
the
waves
and
the
waves
helå
tube
will
generated
come
by
the
fork.
When
thing
to
light
waves
expect.
to
of
the
of
resonance
the
to
the
magnetice
by
current
by
a sine
a
light
as
we
seems
example
of
An
a single
interference
of
soap
the
is
the
combination
thing
value
film.
light.
natural
of
of
two
either
to
be
the
this
is
given
Dark
This
laek
bands
is
advance
will
a current
they
waves
that
appear
represented
the
a consideration
they
aet
of electro-
in
exaetly
that
about
the
same
originate.
with
there
conductor
and
to
see
familiar
is
is
the
fact
a magnetic
oscillatory
oscillations
on water.
These
field.
the
will
a conducIf
field
set
waves
will
up
may
waves
be
velocity
with
whieh
these
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waves
move
-
the
be
just
represented
eurve.
The
by
3.
are
surface
the
phenomenal
We
also
with
the
how
the
resonance
twice
through
we
waves,
having
see
in
light
familiar
us
oscillatory
the
are
The
Fig.
waves
Let
to
interference.,
total
carrying
like
give
passing
Now
tor
We
or
graphically
way.
come
components.
light
, due
we
will
bpe
aBa
and
second
per
emitted
number
the
of
produet
the
to
equal
the length of one wave
J-T
since
N
Anā
since
the
"n
But
|
as
it
to
take
up
the
vibrations.
by
given
is
a circuit
of
period
The
for
order
in
mechanical,
second
the
in
pendulunms
the
as
just
resonance,
in
ve
thus
and
waves
the
as
all
must
station,
sending
the
period
These
circuit.
sending
the
by
receiving
the
for
order
in
same
the
have
must
circuit
its
A
emitted
waves
the
get
to
station
o
work,
wireless
is constant
velocity
rri
In
nÀ
u
U
T =-ar TLC
L
oräer
to
the
tune
the
may
altered.
be
and
to
meter
a waye
calle
resonance
with
another
harmonic
waves
behavior
of
production
might
be
explained
öf
resonance
inferred
on
From
the
and
sound,
that
same
in
the
basis
great
the
by
a circuit
as
final
and
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the
waves
in the
other
ways
it
may
be
they
analysis
tend
of
of
in many
would
kind
any
similarity
electromagnetie
well
as
prođuced
be
may
or motions.,
light,
of
waves
of
length
eireuit.
then,
Resonance,
instrument
an
tuning
aecurate
and
rapid
possible
makes
waves
any
or both
(C)
wave
the
measures
that
has
usually
station
A wireless
with
or the capacity
(L)
inductance
either
resonance
into
eireuit
in
So
capacity.
equals
©
and
inductance
equals
where
to
lead
to
the
belief
in
a Philosophy
that
may
some
day
knowledge.
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inelude
all
-10-
THE STRUCTURE OF THE WAVE METER
HE
It
waves.
the
in
series
so
that
with
movable
coil.
of
wood,
of
the
fixed
along
cut
plates
(MP)
may
rotate
end
over
a scale
as
the
plates
it
is
may
it
to
be
from
fixed
the
throm
in series
by
switeh
The
The
fixed
are
plates
the
it may
rotate.
A
it
that
so
knob
rotated.
and
rotate
to
swing
field
the
to
angles
right
the
with
out
which
tuned.
The
boz
at
put
be
is
coil
are
broken
the
through
the
to
next
portion
projects
whieh
it by
to
rod
movable
whieh
of
blocks
between
movable
The
10.
the
that
sides.
shaded
on
so
the
the
clamped
The
the
by
is
pointer
moves
shown
are
attached
a knob
has
inch
wood
one
rod,
an
of
in Fig.
shown
a brass
to
and
movable
as
plates,
clemped
top
the
that
by
apart
spaced
are
which
blocks
These
figure.
so
of
edges
the
are
which
7,
Fig.
in
FD
marked
plates,
fixed
ten
of
up
made
is
condenser
The
line
ànd
condenser
the
with
series
in
thrown
can be
it
arranged
is
coil
A fixed
coil.
a movable
with
connected
condenser
a variable
of
consists
wireless
resonance
to
circuit
receiving
tuningthe
in
stations
in
used
instrument
an
preceding
the
in
to
referred
is
resonance,
of
discussion
PH
as
meter,
waye
The
HE
front
is
one
movable
with
shown
box
coil
in
that
panel
the
fastened
an
of
opposite
so
that
and variable
coil
it
side
ecan
of
be
condenser
9 &- 10.
contains
is
the
arranged
movable
Figs.
to
the
glass
condenser
so
that
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the
has
panelled
variable
con-
Jl-
denser
is visible.
eross
connected
a
receivers.
the
detector
Now
terminals,
such
since
T
the
s
rotating
the
plates
may
be
tuned
in
resonance
occurs
there
will
tube
or
wave
length
receiving
a maximum
may
be
circuit
read
may
period
varies
with
in
off
then
of
the
9 &
tube
l0,
or
may
be
telephone
circuit
is
given
TCE
a maximum
sounå
Figs.
a Geissler
a
and
be
as
A & B
the
the
capacity,
the
fielå.
cireuit
When resonance
discharge
in
telephone
receivers.
directly
be
the
tuned
on
to
Finis.
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the
the
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r
o
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All use subject to https://about.jstor.org/terms