You have two string segments of equal length, segment 1 of linear mass density \(\mu_{1}\) and segment 2 of linear mass density \(\mu_{2}>\mu_{1}\). You splice the two together and then tie the combination tautly between two posts. You splice in such a way that, once attached to the posts, the length of segment 1 to the left of the splice is the same as the length of segment 2 to the right of the splice. When you pluck at a particular frequency, you set up a standing wave that has this pattern: nodes at the splice and where each segment is attached to its pole plus two more nodes in one of the segments and three more nodes in the other segment (eight nodes in all). What is the numerical value of the ratio \(\mu_{1} / \mu_{2}\) ? \(=\)