A stretched wire has a fundamental frequency f. When it is divided into 3 segments, their fundamental frequencies are f1,f2, and f3. Tension T is constant. We need to find the relation among f,f1,f2,f3. Step 1: Formula for fundamental frequency of a stretched string For a string under tension T, length L, and linear density µ : f=‌
1
2L
√‌
T
µ
Step 2: Frequencies of the three parts Suppose the original length is divided into three parts of lengths L1,L2,L3, so that L=L1+L2+L3 Then their fundamental frequencies are f1=‌
1
2L1
√‌
T
µ
,‌‌f2=‌
1
2L2
√‌
T
µ
,‌‌f3=‌
1
2L3
√‌
T
µ
Step 3: Express Li in terms of fi From the above, Li=‌