Velocity in a wave \(=\sqrt{\frac{T}{\mu}}\)

Fundamental frequency of waves \(\frac{v}{2 l}\)

\(f=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l} \quad \dots (i)\)

If \(T\) decreases by \(19 \%\) value of \(T\) will be \(T-0.19 T\)

Putting this value in \((i)\)

\(f^{\prime}=\sqrt{\frac{T}{\mu}} \frac{(1-0.19)^{1 / 2}}{2 l}\)

\(f^{\prime}=f\left(1-\frac{1}{2} \times 0.19\right)\)

[Binomial theorem]

\(f^{\prime}=f-0.1 f\)

Hence, the frequency decreases by \(0.1 f\) are \(10 \%\) of initial value.