Question

A wave moves with speed $400\text{m/s}$ on a wire , which is under a tension of $900\text{N}$. If the wave moves with $450\text{m/s}$, then the change in tension of the wire is

• A.
  $-250\text{N}$
• B. $+250\text{N}$
• C. $+239\text{N}$
• D. $-239\text{N}$

Answer 1

The correct option is C $+239\text{N}$

Speed of a transverse wave on wire is
$v=\sqrt{\frac{T}{\mu }}......\left(1\right)$
From this, we can write that,
$\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$
$\Rightarrow T_2=T_1\times (\frac{v_2}{v_1}{)}^2$
From the data given in the question,
$T_2=900\times (\frac{450}{400}{)}^2\approx 1139\text{N}$
Then,
$T_2-T_1=1139-900=239\text{N}$
$\therefore$ Tension should be increased by $239\text{N}$
Thus, option (c) is the correct answer.