Answer
$8$ $inches$
Work Step by Step
Let the frequency of a vibrating string be $F$
Constant tension be $k$
And the length be $l$
We can write the relation: $F=\frac{k}{l}$
If
$l=12in$
$F=440$ times per second
$k$ is unknown
$440=\frac{k}{12}$
$k=440\times12$
$k=5280$
We get general form: $F=\frac{5280}{l}$
If $F=660$
$660=\frac{5280}{l}$
$l=\frac{5280}{660}$
$l=8in$
