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 $V / 4$ . The value of T is closed to

Moderate

A

$10.2 \times 10^{2} N$
B

$1.2875 \times 10^{3} N$
C

$2.50 \times 10^{4} N$
D

$1 \times 10^{4} N$

Solution

$V = \sqrt{\frac{T}{μ}} ∴ V \propto \sqrt{T} \Rightarrow \frac{V_{1}}{V_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow \frac{V}{\frac{V}{4}} = \sqrt{\frac{T}{T^{1}}} \Rightarrow 16 = \frac{T}{T^{1}} \Rightarrow T^{1} = \frac{T}{16} = \frac{2.06 \times 10^{4}}{16} = 0.12875 \times 10^{4} = = 1.2875 \times 10^{+ 3} N$

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