A wave moves with speed 300 $m{s}^{-1}$  on a wire which is under a tension of 50 N. By how much the tension must be changed, in newton, to increase the speed to 312$m{s}^{-1}$  ? Round off to nearest integer)

Speed of a transverse wave on a wire is given by
 $\text{υ=}\sqrt{\frac{\text{T}}{\text{μ}}}\mathrm{....}\left(1\right)$
Differentiating with respect to tension, we have 
 $\frac{\text{dυ}}{\text{dT}}\text{=}\frac{\text{1}}{\text{2}\sqrt{\text{μT}}}\mathrm{...}\left(2\right)$
Dividing Equation (2) by Equation (1), we get
 $$\begin{gathered} \frac{\text{dυ}}{\text{υ}}\text{=}\frac{\text{1}}{\text{2}}\frac{\text{dT}}{\text{T}} \\ \Rightarrow \text{dT=}\left(\text{2T}\right)\frac{\text{dυ}}{\text{υ}} \end{gathered}$$
 Substituting the values, we get
 $\text{dT=}\frac{\left(\text{2}\right)\left(\text{50}\right)\left(\text{312-300}\right)}{\text{300}}\text{=4N}$
So, tension must be increased by 4 N