$($Problem $13\mathrm{.}2\mathrm{.}2)$ Out of Tune. The A string of a violin is a little tightly stretched and therefore out of tune. Beats at

$4\mathrm{.}00$Hz are heard when the string is strung along with an identical violin that is tuned properly and therefore is

oscillating accurately at concert A $(440$Hz$).$

$($a$)$ What is the frequency of the out$-$of$-$tune violin

string?

$($b$)$ What is the period of the out$-$of$-$tune violin

string oscillation?

$($c$)$ What is the fractional difference in the tension between the

in$-$tune and out$-$of$-$tune strings?