A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104 N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

Engineering

Physics

Prograssive Wave Equation

Wave Velocity on Stretched String

Question

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 10⁴ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

10.2 × 10² N

30.5 × 10⁴ Ns

5.15 × 10³ N

2.50 × 10⁴ N

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$v \propto \sqrt{T}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow \frac{v}{(v / 2)} = \sqrt{\frac{2 .06 \times 10^{4}}{T}}$

$\Rightarrow T = \frac{2 .06 \times 10^{4}}{4} N = 0 .515 \times 10^{4} N$