Speed of a pulse in a string

1. Wave
Speed
of
a
String

2. Weighted
ropes
are
o2en
used
in
strength
training.
The
user
rapidly
moves
these
heavy
ropes
up
and
down
crea;ng
pulses
that
moves
down
the
rope.
(
The
user
applies
a
tension
force
to
the
rope.
)

3. Wave
Speed
Equa;on
• Wave
speed
is
given
by
the
formula:
• v
=
√(Ts/μ)
• Here
v
=
speed
in
m/s
• Ts
=
Tension
in
the
string
• μ
=
liner
mass
density
• Linear
mass
density
can
be
calculated
by
dividing
the
mass
of
the
string
by
its
length.

4. Ques;on
1
• What
would
happen
to
the
wave
speed
if
the
tension
(Ts)
was
to
be
quadrupled
?
1) The
speed
would
triple
2) The
speed
would
double
3) The
sped
would
not
change

5. Answer:
2
Reason:
As
observed
in
the
formula,
√(Ts/μ),
increasing
the
Tension
by
a
factor
of
4
would
cause
the
speed
to
increase
by
a
a
factor
of
(4)1/2.
Which
is
equal
to
2.

6. Ques;on
2
• What
would
happen
to
the
speed
of
the
wave
if
the
mass
of
the
string
was
quadrupled,
but
the
length
and
tension
input
was
the
same?
1) The
speed
would
half.
2) The
speed
would
double
3) The
speed
would
increase
by
21/2

7. Answer:
1
The
the
Tension
exerted
by
the
user
would
s;ll
be
the
same,
however
the
linear
mass
density
of
the
rope
would
change
by
a
factor
of
4.
Thus,
the
speed
would
change
by
a
factor
of
(1/4)1/2,
which
equals
½
.

8. Ques;on
3
• If
the
two
ropes
have
a
combined
mass
of
9kg
and
are
4m
long
each,
what
is
the
tension
force
applied
by
the
user
to
the
rope
when
the
pulse
speed
is
calculated
to
be
8m/s?

9. How
to
solve
1. Calculate
the
linear
mass
density:
μ=
m/L
μ=
(9/2)/4
μ=1.125kg/m
2.
v
=
√(Ts/μ)
8=√(Ts/1.125)
64=Ts/1.125
72N=
Ts