Physics - Sound Wave Question with Solution | TestHub

For vibrating tunning fork over a resonance tube, the first resonance is obtained at the length
$$l_1=\frac{\lambda }{4}$$ and for second resonance,
$${\mathrm{l}}_2=\frac{\lambda }{4}+\frac{\lambda }{2}=\frac{3\lambda }{4}$$ From Eq. (i) and (ii), we get $$\begin{array}{cc}& {\mathrm{l}}_2-{\mathrm{l}}_1=\frac{3\lambda }{4}-\frac{\lambda }{4}=\frac{\lambda }{2}\\ \Rightarrow & \lambda =2\left(l_2-l_1\right)\\ \Rightarrow & \mathrm{v}=2\mathrm{f}\left({\mathrm{l}}_2-{\mathrm{l}}_1\right)\end{array}$$ ..(iii) $\left(\because \lambda =\frac{\mathrm{v}}{\mathrm{f}}\right)$ Here, $\mathrm{f}=800\mathrm{Hz},{\mathrm{l}}_1=9.75\mathrm{cm},{\mathrm{l}}_2=31.25\mathrm{cm}$ Substituting the given values in Eq. (iii), we get $$\begin{array}{rl}& \Rightarrow \mathrm{v}=2\times 800(31.25-9.75)\\ & =34400\mathrm{cm}/\mathrm{s}=344\mathrm{m}/\mathrm{s}\end{array}$$