Question

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

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

Answer 1

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

Given, when velocity of the wave is $v$, tension in the wire, $=2.06\times {10}^{4}N$

And when velocity becomes $\frac{v}{2}$, tension becomes $T$.

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

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

$4T=2.06\times {10}^4$

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

Final answer: (b)