21.45. Model: The steel wire is under tension and it vibrates with ...

northalligatorUrban and Civil

Nov 29, 2013 (3 years and 6 months ago)

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21.45.
Model: The steel wire is under tension and it vibrates with three antinodes.
Visualize: Please refer to Figure P21.45.
Solve: When the spring is stretched 8.0 cm, the standing wave on the wire has three antinodes. This means
λ
3
2
3
= L
and the tension T
S
in the wire is T
S
= k(0.080 m), where k is the spring constant. For this tension,
v
T
wire
S
=
µ
⇒ =f
T
λ
µ
3
S
⇒ =
( )
f
L
k
3
2
0.08 m
µ
We will let the stretching of the spring be ∆x when the standing wave on the wire displays two antinodes. This
means λ
2
= L and

=T kx
S
. For the tension

T
S
,

=

⇒ =

v
T
f
T
wire
S S
µ
λ
µ
2
⇒ =f
L
k x1 ∆
µ
The frequency f is the same in the above two situations because the wire is driven by the same oscillating magnetic
field. Now, equating the two frequency equations,
1 3
2L
k x
L
k

µ µ
=
( )
0.080 m
⇒ = =∆x 0.18 m 18 cm