The fundamental frequency of vibration of $1\text{ cm}$ long string is $256\text{ Hz}$. If the length of the…

The fundamental frequency of vibration of $1\text{ cm}$ long string is $256\text{ Hz}$. If the length of the string is reduced to $1/4\text{ cm}$ keeping the tension unaltered, the new fundamental frequency will be
  1. 256 Hz
  2. 512 Hz
  3. 1024 Hz
  4. 2048 Hz

Solution

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

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