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  4. A string in a musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of 1000 Hz is to be produced, then required length of string is

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Q. A string in a musical instrument is $50\, cm$ long and its fundamental frequency is $800\, Hz$. If a frequency of $1000\, Hz$ is to be produced, then required length of string is

JIPMERJIPMER 2010Waves

Solution:

Fundamental frequency $\upsilon = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$
$\upsilon \propto \frac{1}{L} \, \therefore \frac{800}{1000} = \frac{L'}{50}$
$L' = \frac{800 \times 50}{1000} = 40 \, cm$