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
$v=\sqrt{\frac{T}{\mu }}......\left(1\right)$
Differentiating with respect to time on both sides,
$\frac{dv}{dt}=\frac{1}{2\sqrt{\mu T}}\frac{dT}{dt}.........\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$ we have

$\frac{dv}{v}=\frac{1}{2}\frac{dT}{T}$

$\Rightarrow dT=2T\times \frac{dv}{v}$
From the data given in the question ,
$dT=2\times 900\times \frac{(450-400)}{400}=+225\text{N}$
$\therefore$ Tension should be increased by $225\text{N}$
Thus, option (c) is the correct answer.