Consider two strings which are adjusted to support standing waves at exactly $220$ Hz$.$ If one of the strings is then loosened slightly, a beat frequency of $3$ beats per second results.$$ What is the frequency of the recently tightened string?

Group of answer choices

$217$ Hz

$223$ Hz

$217$ Hz or $223$ Hz$,$ no way to tell with given information

$220\mathrm{.}3$ Hz

$219\mathrm{.}6$ Hz

$220\mathrm{.}3$ Hz or $219\mathrm{.}6$ Hz$,$ no way to tell with given information