$11.$ A thin, light string supports a weight $\backslash ($ W $\backslash )$ hanging from the ceiling. In this situation, the string produces a note of frequency $\backslash ($ f $\backslash )$ when vibrating in its fundamental mode. In order to cause this string to produce a note one octave higher in its fundamental mode without stretching it$,$ we must change the weight to

A$.\backslash (4$ W $\backslash ).$

B$.\backslash (2$ W $\backslash ).$

C$.\backslash (\backslash$sqrt$\{2\}$ W $\backslash ).$

D$.\backslash ($ W $/2\backslash ).$

E$.\backslash ($ W $/4\backslash ).$