A $1\text{ cm}$ long string vibrates with fundamental frequency of $256\text{ Hz}$. If the length is reduced…

A $1\text{ cm}$ long string vibrates with fundamental frequency of $256\text{ Hz}$. If the length is reduced to $1/4\text{ cm}$ keeping the tension unaltered, the new fundamental frequency will be (in Hz)
  1. 64
  2. 256
  3. 512
  4. 1024

Solution

We have, $n \propto \frac{1}{l} \Rightarrow \frac{l_2}{l_1} = \frac{n_1}{n_2}$ $\therefore\text{ Fundamental frequency, }n_2 = \frac{l_1}{l_2} n_1 = \frac{1 \times 256}{1 / 4} = 1024\text{ Hz}$

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