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 [2022]

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Solution

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 [2022]

1 1 : 1

2 $\sqrt{2} : 1$

3 $1 : \sqrt{2}$

4 1 : 2

Ans.
(3)

Velocity of a transverse wave in a stretched string is given by

$v = \sqrt{\frac{T}{μ}}$ ...(i)

Where $T$ is the tension in the string and $μ$ is the mass per unit length of the string.

If tension $T$ is doubled, then final speed of the wave in the string will be,

$v' = \sqrt{\frac{2 T}{μ}}$ ...(ii)

From eq. (i) and (ii)

$\frac{v}{v'} = \frac{1}{\sqrt{2}}$

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