Question

A wire is $4\text{m}$ long and has a mass of $0.2\text{kg}$. 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 $0.8\text{sec}$. The tension is the cord will be

• A. $80\text{N}$
• B. $160\text{N}$
• C. $240\text{N}$
• D. $320\text{N}$

Answer 1

The correct option is A $80\text{N}$

Distance travelled in $4$ trips will be $32\text{m}$
$t=\frac{d}{v}\Rightarrow v=\frac{d}{t}=\frac{32}{0.8}=40\text{m/s}$
Velocity of sound wave is
$v=\sqrt{\frac{T}{\mu }}\Rightarrow T=\mu v^2$
$T=\frac{0.2}{4}\times (40{)}^2=\frac{2\times 16\times 10}{4}$
$T=80\text{N}$