Answer
$x_1=0.042m$
$x_2=0.0818m$
$x_3=0.119m$
$x_4=0.155m$
$x_5=0.188m$
$x_6=0.220m$
Work Step by Step
For all frequencies, the velocity is constant.
Frequency of the unfingered string is $f=v\lambda$
$\lambda=2l$
$\frac{f_u}{f_1}=2^{\frac{1}{12}}=\frac{v\lambda_u}{v\lambda_1}=\frac{2l_u}{2l_1}$
$l_1=\frac{l_u}{2^{\frac{1}{12}}}=\frac{0.75m}{2^{\frac{1}{12}}}=0.708m$
$x_1=0.042m$
$l_2=\frac{l_1}{2^{\frac{1}{12}}}=0.668m$
$x_2=0.0818m$
$l_3=\frac{l_2}{2^{\frac{1}{12}}}=0.631m$
$x_3=0.119m$
$l_4=\frac{l_3}{2^{\frac{1}{12}}}=0.595m$
$x_4=0.155m$
$l_5=\frac{l_1}{2^{\frac{1}{12}}}=0.562m$
$x_5=0.188m$
$l_6=\frac{l_1}{2^{\frac{1}{12}}}=0.530m$
$x_6=0.220m$
