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  4. If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :

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Q. If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :

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Solution:

$v \propto \sqrt{\text { Tension }}$
$\frac{ v _{ i }}{ v _{ f }}=\sqrt{\frac{ T _{ i }}{ T _{ f }}}$
$\frac{ v _{ i }}{ v _{ f }}=\sqrt{\frac{ T }{2 T }}$
$\frac{ v _{ i }}{ v _{ f }}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$