If the initial tension on a stretched string | vedclass

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(B) The speed of a transverse wave on a stretched string is given by the formula $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the

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$ 1 : \sqrt{2} $

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(B) The speed of a transverse wave on a stretched string is given by the formula $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Since $\mu$ remains constant,the speed is directly proportional to the square root of the tension: $v \propto \sqrt{T}$.Let the initial tension be $T_i = T$ and the final tension be $T_f = 2T$.The ratio of the initial speed $v_i$ to the final speed $v_f$ is given by:$\frac{v_i}{v_f} = \sqrt{\frac{T_i}{T_f}}$Substituting the values,we get:$\frac{v_i}{v_f} = \sqrt{\frac{T}{2T}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$Thus,the ratio is $1 : \sqrt{2}$.

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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