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A sonometer wire has a total length of 1...

A sonometer wire has a total length of 1 m between the fixed ends. Where should the two bridges be placed below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 2 : 3 ?

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To solve the problem of placing two bridges on a sonometer wire of length 1 meter so that the three segments of the wire have their fundamental frequencies in the ratio 1:2:3, we can follow these steps: ### Step 1: Understand the relationship between frequency and length The fundamental frequency (f) of a vibrating string is inversely proportional to its length (L). This means that if the frequencies are in the ratio 1:2:3, then the lengths of the segments (L1, L2, L3) must be in the ratio of the inverse of the frequencies. ### Step 2: Set up the ratios Given the frequencies are in the ratio 1:2:3, we can express the lengths of the segments as: - L1 is proportional to 1 (1 part) ...
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