Physics - Wave on String Question with Solution | TestHub

The frequency of a stretched wire is given by $f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

This implies $f\propto \sqrt{T}$

Given that the tension is increased by $25\%$, the new tension is $T^{\prime }=T+0.25T=1.25T$

The new frequency is $f^{\prime }=\sqrt{\frac{1.25T}{T}}f=\sqrt{1.25}f$

Comparing with $f^{\prime }=nf$, we get $n=\sqrt{1.25}$

Answer: $\sqrt{1.25}$