Physics - Sound Wave Question with Solution | TestHub

The frequency of a vibrating wire $\mathrm{f}=\frac{1}{2l}\sqrt{\frac{\mathrm{T}}{\mathrm{m}}}$ $$\therefore \mathrm{f}\propto \frac{1}{l}\Rightarrow \mathrm{fl}=\text{ constant }$$ Let the frequency of the fork be $f$ and the initial and final frequencies of the wire be $f_1$ and $f_2$. The number of beats heard before decreasing the length is $f-f_1=3$ The number of beats after decreasing the length is ${\mathrm{f}}_2-\mathrm{f}=3$ $$\begin{array}{ll}\therefore & {\mathrm{f}}_1{l}_1={\mathrm{f}}_2{l}_2\\ \therefore & (\mathrm{f}-3)50=(\mathrm{f}+3)49\\ & 50\mathrm{f}-49\mathrm{f}=147+150\\ \therefore & \mathrm{f}=297\mathrm{Hz}\end{array}$$