My submission for LO6, a word problem with solution

1. Physics
101
LO6
–
Vibrato
To
achieve
vibrato,
a
slight
rapid
change
of
pitch
in
a
sustained
note,
players
of
string
instruments
wiggle
their
finger
very
slightly
back
and
forth.
This
quickly
shortens
and
lengthens
the
string,
altering
the
pitch.
This
is
an
important
skill
for
a
musician
as
it
creates
richer
tone
and
more
pleasant
sounds.
If
a
violinist
is
playing
C4
(frequency
261.6
Hz)
by
how
much
does
the
frequency
change
when
she
creates
vibrato
by
rolling
her
fingertip
back
and
forth
(her
fingertip
length
is
1cm).
The
tension
in
the
violin
string
is
60N
and
the
linear
density
of
the
string
is
1.50
g/m.
(Note
C4
is
the
second
harmonic)

2. Physics
101
LO6
–
Vibrato
(Solution)
To
achieve
vibrato,
a
slight
rapid
change
of
pitch
in
a
sustained
note,
players
of
string
instruments
wiggle
their
finger
very
slightly
back
and
forth.
This
quickly
shortens
and
lengthens
the
string,
altering
the
pitch.
This
is
an
important
skill
for
a
musician
as
it
creates
richer
tone
and
more
pleasant
sounds.
If
a
violinist
is
playing
C4
(frequency
261.6
Hz)
by
how
much
does
the
frequency
change
when
she
creates
vibrato
by
rolling
her
fingertip
back
and
forth
(her
fingertip
length
is
1cm).
The
tension
in
the
violin
string
is
60.0N
and
the
linear
density
of
the
string
is
1.50
g/m.
1. Parse
the
Problem,
convert
to
MKS
units
-­‐ f1
=
261.6
Hz
-­‐ ΔL
=
±0.005
m
-­‐ T
=
60.0N
μ
=
0.00150
kg/m
2. Identify
relevant
equations
𝑓! =
!
!"
!
!
3. Solve
𝑓! =
!
!!
!
!
L =
!
!!
!
!
=
!
!(!"#.!)
!!.!
!.!!"#!
= 0.382 m
Lowest
frequency:
𝑓! =
!
!(!.!"#!!.!!")
!!.!
!.!!"#!
= 258.4 Hz
Highest
Frequency:
𝑓! =
!
!(!.!"#!!.!!")
!!.!
!.!!"#!
= 265.2 Hz
The
frequency
changes
by
-­‐3.2
Hz
and
+3.6
Hz
during
vibrato