Q141 / 160 · AP EAMCET 2023 (15 May Shift 2) · Physics

A string of length ' $L$ ' is stretched by $\frac{L}{20}$ and the speed of transverse waves along it is ' $v$ '. The speed of wave when it is stretched by $\frac{\mathrm{L}}{10}$ will be (assume that Hooke's law is applicable)

  • A
    $2 \mathrm{v}$
  • B
    $\frac{\mathrm{v}}{\sqrt{2}}$
  • Correct answer
    C
    $\mathrm{v} \sqrt{2}$
  • D
    $4 v$

Solution

$\begin{aligned} & v \propto \sqrt{\mathrm{T}} \\ & \mathrm{T} \propto \Delta \mathrm{l} \\ & v \propto \sqrt{\Delta \mathrm{l}}\end{aligned}$ $\begin{aligned} & \frac{\mathrm{v}_2}{\mathrm{v}_1}=\sqrt{\frac{\Delta \mathrm{l}_2}{\Delta \mathrm{l}_1}}=\sqrt{\frac{\frac{\mathrm{L}}{10}}{\mathrm{~L}}} \\ & \mathrm{v}_2=v \sqrt{2}\end{aligned}$

Hence, the correct answer is option: 'C'.

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