13. A string is fixed at both ends. On increasing the tension in the string by 2.5 N , the fundamental frequency is altered in the ratio of \( 3: 2 \). What is the original stretching force? (Ans: 2 N )

When analyzing a string fixed at both ends, the fundamental frequency \( f \) is related to the tension \( T \) by the equation \( f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \), where \( L \) is the length of the string and \( \mu \) is the mass per unit length. If the tension increases by 2.5 N and the frequency ratio changes to \( \frac{3}{2} \), you can set up the following relationship to solve for the original tension. Using the ratios of the squares of the frequencies gives us an equation involving the original and the new tension. By substituting the known values into the equation, you can arrive at the original stretching force being 2 N, creating a happy ending!