= Solution
Let $T$ be the common <tension> and $\mu_j$ the <linear mass densities>. The <characteristic impedance of a stretched string> is $Z_j=T/c_j=\sqrt{T\mu_j}$. Continuity of <displacement> and transverse <force> at a massless junction gives $1+r=t$ and $Z_1(1-r)=Z_2t$. Consequently
$$
r=\frac{Z_1-Z_2}{Z_1+Z_2}=\frac{1-\sqrt3}{1+\sqrt3},\qquad
\boxed{\mathcal R=|r|^2=(2-\sqrt3)^2=0.07180.}
$$
\b[The reflected <power> is $7.18\%$.] The minus sign of $r$ represents a phase reversal, not negative <power>. Both incident and reflected <waves> travel in the first string, so their <power> ratio is simply the squared displacement-amplitude ratio. As a check, $\mathcal T=(Z_2/Z_1)|t|^2=0.92820$ and $\mathcal R+\mathcal T=1$.
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