Question

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

• A. $2.50\times {10}^4\text{N}$
• B. $5.15\times {10}^3\text{N}$
• C. $30.5\times {10}^4\text{N}$
• D. $10.2\times {10}^2\text{N}$

Answer 1

The correct option is B $5.15\times {10}^3\text{N}$

The velocity of a transverse wave in a stretched wire is given by

$v=\sqrt{\frac{T}{\mu }}$

Where,

$T=\text{Tension in the wire}$

$\mu =\text{linear density of wise}$

$(\because v\propto T)$

$\therefore \frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$

$\Rightarrow \frac{v}{v/2}=\sqrt{\frac{2.06\times {10}^4}{T_2}}$

$\Rightarrow T_2=\frac{2.06\times {10}^4}{4}=0.515\times {10}^4\text{N}$

$\Rightarrow T_2=5.15\times {10}^3\text{N}$