Q120 / 200 · NEET 2022 (Phase 1) · Physics

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:

Solution

Case 1:

$T_{1} = T$

Case 2:

$T_{2} = 2 T$

We know, speed of transverse wave is related to tension by

$v = \sqrt{\frac{T}{μ}}$ , here, $μ$ is mass per unit length of the string.

$∴ \frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{T}{2 T}} = \frac{1}{\sqrt{2}} = 1 : \sqrt{2}$

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