P17_021.PDF

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21. The pulses have the same speed
v.
Suppose one pulse starts from the left end of the wire at time
t
= 0.
Its coordinate at time
t
is
x
1
=
vt.
The other pulse starts from the right end, at
x
=
L,
where
L
is the
length of the wire, at time
t
= 30 ms. If this time is denoted by
t
0
then the coordinate of this wave at time
t
is
x
2
=
L
−
v(t
−
t
0
). They meet when
x
1
=
x
2
, or, what is the same, when
vt
=
L
−
v(t
−
t
0
). We solve
for the time they meet:
t
= (L +
vt
0
)/2v and the coordinate of the meeting point is
x
=
vt
= (L +
vt
0
)/2.
Now, we calculate the wave speed:
v
=
τL
=
m
(250 N)(10.0 m)
= 158 m/s
.
0.100 kg
Here
τ
is the tension in the wire and
L/m
is the linear mass density of the wire. The coordinate of the
meeting point is
10.0 m + (158 m/s)(30
×
10
−3
s)
x
=
= 7.37 m
.
2
This is the distance from the left end of the wire. The distance from the right end is
L
−
x
= 10 m
−
7.37 m = 2.63 m.

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