First slide

Travelling wave

Question

A transverse wave travels on a taut steel wire with velocity of V when tension in it is $2.06 \times 10^{4} N$ . When the tension is changed to T. The velocity changed to $V / 2$ the value of T is close to _____ $\times 10^{3} N$

Moderate

Solution

Velocity of transverse wave is given by v
$V \propto \sqrt{T} v = \sqrt{\frac{T}{μ}} \Rightarrow \frac{V_{1}}{V_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} S . B . S \Rightarrow \frac{V_{1}^{2}}{V_{2}^{2}} = \frac{T_{1}}{T_{2}} \Rightarrow \frac{V^{2}}{{(\frac{V}{2})}^{2}} = \frac{T_{1}}{T_{2}} \Rightarrow T_{2} = \frac{T_{1}}{4} \Rightarrow T_{2} = \frac{2.06 \times 10^{4}}{4} = 5.15 \times 10^{3} N$

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