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  4. A stretched string resonates with tuning fork frequency 512 Hz when length of the string is 0.5 m. The length of the string required to vibrate resonantly with a tuning fork of frequency 256 Hz would be

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Q. A stretched string resonates with tuning fork frequency $512 \,Hz$ when length of the string is $0.5 \,m$. The length of the string required to vibrate resonantly with a tuning fork of frequency $256\, Hz$ would be

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Solution:

$f=\frac{1}{2 l}\left[\frac{T}{\mu}\right]^{\frac{1}{2}}$ when $f$ is halved, the length is doubled
$\therefore $ Length is $1 m$.