Physics - Sound Wave Question with Solution | TestHub

${\nu }_1=256\mathrm{ }\mathrm{H}\mathrm{z}$

For tuning for ${\nu }_2-{\nu }_1=\pm 5,$

${\nu }_2=\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{p}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{o}$

${\nu }_2=\left(256+5\right) \mathrm{H}\mathrm{z}\mathrm{ }\mathrm{o}\mathrm{r}\mathrm{ }\left(256-5\right) \mathrm{H}\mathrm{z}$

${\nu }_2=261 \mathrm{Hz}$ or $251 \mathrm{Hz}$

When tension is increased, the beat frequency decreases to $2$ beats ${\mathrm{s}}^{-1}$.

If we assume that the frequency of the piano string is $261 \mathrm{Hz}$, then on increasing tension, frequency, more than $261 \mathrm{Hz}$. But it is given that beat frequency decreases to $2$, therefore, $261$ is not possible.

Hence, $251 \mathrm{Hz}$ was the frequency of the piano string before increasing tension.