A transverse wave travels on a taut steel wir | vedclass

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Question

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

Vedclass · Accepted Answer

$5.15 	imes 10^{3} \; N$

Vedclass · Answer

(B) The velocity of a transverse wave on a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.From this relation,we see that $v \propto \sqrt{T}$.Let the initial tension be $T_1 = 2.06 	imes 10^{4} \; N$ and the initial velocity be $v_1 = v$.Let the final tension be $T_2 = T$ and the final velocity be $v_2 = v/2$.Using the proportionality $v \propto \sqrt{T}$,we can write: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$.Substituting the given values: $\frac{v/2}{v} = \sqrt{\frac{T}{2.06 	imes 10^{4}}}$.$\frac{1}{2} = \sqrt{\frac{T}{2.06 	imes 10^{4}}}$.Squaring both sides: $\frac{1}{4} = \frac{T}{2.06 	imes 10^{4}}$.$T = \frac{2.06 	imes 10^{4}}{4} = 0.515 	imes 10^{4} = 5.15 	imes 10^{3} \; N$.

$A$ transverse wave travels on a taut steel wire with a velocity of $v$ when the tension in it is $2.06 \times 10^{4} \; N$. When the tension is changed to $T$,the velocity changes to $v/2$. The value of $T$ is close to:

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