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The length of the string of a musical instrument is 90 cm and has a fundamental frequency of 120 Hz. Where should it be pressed to produce fundamental frequency of 180 Hz?

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80 cm

75 cm

60 cm

45 cm

answer is C.

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Detailed Solution

Frequency of stretched string

$n = \frac{1}{2 ℓ} \sqrt{\frac{T}{m}}$

If T and m are constant

$\begin{array}{l} n \propto \frac{1}{ℓ} \\ \frac{n^{'}}{n} = \frac{ℓ}{ℓ^{'}} \\ \frac{180}{120} = \frac{90}{ℓ^{'}} \\ ℓ^{'} = 60 cm \end{array}$

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