The extension in a string obeying Hooke’s law is $x$. The speed of transverse waves in the stretched string…

The extension in a string obeying Hooke’s law is $x$. The speed of transverse waves in the stretched string is $v$. If the extension in the string is increased to $1.5\,x$, the speed of transverse waves in it will be
  1. 1.22 $v$
  2. 2 $v$
  3. 1.5 $v$
  4. $v$

Solution

As, $v \propto \sqrt{T}$, so $T \propto x$ $\therefore \frac{v'}{v} = \sqrt{\frac{1.5 x}{x}}$ $\Rightarrow v' = \sqrt{1.5} \cdot v = 1.22 v$

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