First slide

Travelling wave

Question

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

Easy

A

$5.15 x 10^{3} N$
B

$10.2 x 10^{2} N$
C

$2.50 x 10^{4} N$
D

$30.5 x 10^{4} N$

Solution

$\begin{array}{l} S p e e d o f w a v e o n s t r i n g, v \propto \sqrt{T} \\ \frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \\ \Rightarrow \frac{v}{(v / 2)} = \sqrt{\frac{2.06 \times 10^{4}}{T}} \\ \Rightarrow T = \frac{2.06 \times 10^{4}}{4} N = 0.515 \times 10^{4} N \end{array}$
$\Rightarrow T = 5.15 x 10^{3} N$

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