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Show that when a string fixed at its two...

Show that when a string fixed at its two ends vibrates in 1 loops, 2 loops , 3 loops and 4 loops , the frequencies are in the ratio `1:2:3:4.`

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To show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops, and 4 loops, the frequencies are in the ratio 1:2:3:4, we can follow these steps: ### Step 1: Understand the formula for frequency The frequency of a vibrating string fixed at both ends is given by the formula: \[ f_n = \frac{n}{2L} \sqrt{\frac{T}{m}} \] where: - \( f_n \) is the frequency of the nth harmonic, - \( n \) is the number of loops (or harmonics), ...
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