Physics - Wave on String Question with Solution | TestHub

$$ f$=\frac{$ V$}{2\ell }=\frac{1}{2\ell }\sqrt{\frac{$ T$}{\mu }}=\frac{1}{2\ell }\sqrt{\frac{$ T$}{$ Ad$}}$

Also,$$ Y$=\frac{$ T$\ell }{$ A$\Delta \ell } \Rightarrow \frac{$ T$}{$ A$}=\frac{$ Y$\Delta \ell }{\ell } \Rightarrow $ f$=\frac{1}{2\ell }\sqrt{\frac{\text{Y}\Delta \ell }{\ell \text{d}}}$

$\ell =\text{1.5 m, }\frac{\Delta \ell }{\ell }=\text{0.01, d}=\text{7.7}\times 10^{\mathrm{3 }}\text{kg}/{\text{m}}^3$

$\text{Y}=\text{2.2}\times 10^{1\mathrm{1 }}\text{N}/{\text{m}}^2$

After solving

$$ f$=\sqrt{\frac{2}{7}}\times \frac{10^3}{3}$ \text{H}\text{z}$$

$$ f$ \approx \text{178.2 }$ \text{H}\text{z}$$