The length of the string of a musical instrument is $90\text{ cm}$ and has a fundamental frequency of…

The length of the string of a musical instrument is $90\text{ cm}$ and has a fundamental frequency of $120\text{ Hz}$. Where should it be pressed to produce fundamental frequency of $180\text{ Hz}$? [NEET 2020]
  1. 75 cm
  2. 60 cm
  3. 45 cm
  4. 80 cm

Solution

Given, length of string of musical instrument, $l_1 = 90\text{ cm} = 0.9\text{ m}$ Fundamental frequency, $f_1 = 120\text{ Hz}$ $f_2 = 180\text{ Hz}$ As, $f \propto \frac{1}{l} \Rightarrow \frac{f_1}{f_2} = \frac{l_2}{l_1}$ $\Rightarrow l_2 = \frac{f_1 l_1}{f_2} = \frac{120 \times 0.9}{180}$ $\Rightarrow l_2 = \frac{2}{3} \times 0.9 = 0.6\text{ m} = 60\text{ cm}$

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