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Two identical strings X and Z made of the same material have a tension $T_{X}$ and $T_{Z}$ in them. If their fundamental frequencies are 450 Hz and 300 Hz respectively, the ratio $T_{X} / T_{Z}$ is

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$2.25$

0.44

1.25

1.5

answer is A.

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Detailed Solution

Using $f = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
Where, T= tension and $μ = \frac{mass}{length}$
$f_{x} = \frac{1}{2 l} \sqrt{\frac{T_{x}}{μ}}$ and $f_{z} = \frac{1}{2 l} \sqrt{\frac{T_{z}}{μ}}$

$\frac{f_{x}}{f_{z}} = \frac{450}{300} = \sqrt{\frac{T_{x}}{T_{z}}}$

$∴ \frac{T_{x}}{T_{z}} = \frac{9}{4} = 2.25$

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