14. waves and sound — Physics STD 11 Science — Question

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.