Question

A wave moves with speed 300 m/s on a wire which is under a tension of 500 N. Find how much the tension must be changed to increase the speed to 312 m/s?

• A. 6.67 N
• B. 7.12 N
• C. 8.34 N
• D. 9.12 N

Answer 1

Answer: (A)

. 6.67 N.

Speed of a transverse wave on a wire is,

$v=\sqrt{\frac{T}{\mu }}$ .....(i)

Differentiating with respect to tension, we have

$\frac{dv}{dT}=\frac{1}{2\sqrt{\mu T}}$

Dividing Eq.(ii) by Eq.(i), we have

$\frac{dv}{v}=\frac{1}{2}\frac{dT}{T}$
or $dT=\left(2T\right)\frac{dv}{v}$

Substituting the proper values, we have

$dT=\frac{\left(2\right)\left(500\right)(312-300)}{300}=6.67N$

i.e., tension should be increased by 6.67 N.