Question

A wire is $4 \, m$ long and has a mass $0.2 \, kg$ . The wire is kept horizontally. A transverse pulse is generated by plucking one end of the taut (tight) wire. The pulse makes four trips back and forth along the cord in $0.8 \, sec$ . The tension in the cord will be

• A. $80 \, N$
• B. $160 \, N$
• C. $240 \, N$
• D. $320 \, N$

Answer 1

Answer: (A)

$4$ trips means $32 \, m$

Wave speed is,
$v=\frac{d}{t}=\frac{32}{0.8}=40 \, m \, s^{- 1}$
$v=\sqrt{\frac{T}{\mu }}$
Therefore, tension in the cord is,
$T=\mu v^{2}$
$T=\frac{0.2}{4}\times \left(40\right)^{2}=\frac{2 \times 16 \times 10}{4}$
$T=80 \, N$