A wire stretched between two ends of a sonometer wire is of length 200 cm. What should be the position of wedges so that the fundamental frequency of three parts will have the ratio 1 : 3 : 5.

Explanation

To solve the problem of finding the positions of the wedges on a sonometer wire such that the fundamental frequencies of the three parts have the ratio 1:3:5, we can follow these steps:

### Step 1: Understanding the relationship between frequency and length
The frequency of a vibrating string is inversely proportional to its length. Therefore, if we denote the lengths of the three parts as \( L_1 \), \( L_2 \), and \( L_3 \), we can express the ratios of their frequencies as:
\[ f_1 : f_2 : f_3 = \frac{1}{L_1} : \frac{1}{L_2} : \frac{1}{L_3} \]
Given the frequency ratio \( 1 : 3 : 5 \), we can write:
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