Question:
A transverse wave travels on a taut steel wire with a velocity of $v$ when tension in it is $2.06 \times 10^{4} \mathrm{~N}$. When the tension is changed to $T$, the velocity changed to $v / 2$. The value of $T$ is close to:
Correct Option: , 2
Solution:
(2) The velocity of a transverse wave in a stretched wire is given by
$v=\sqrt{\frac{T}{\mu}}$
Where,
$T=$ Tension in the wire
$\mu=$ linear density of wire
$(\because V \propto T)$
$\therefore \frac{v_{1}}{v_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}$
$\Rightarrow \frac{v}{v} \times 2=\sqrt{\frac{2.06 \times 10^{4}}{T_{2}}}$
$\Rightarrow T_{2}=\frac{2.06 \times 10^{4}}{4}=0.515 \times 10^{4} \mathrm{~N}$
$\Rightarrow T_{2}=5.15 \times 10^{3} \mathrm{~N}$