• # question_answer In a ball, a person receives direct sound waves from a source 120 m away. He also receives wave from the same source which reach him after being reflected from one 25 m high ceiling at a point half-way between them. The two waves interfere constructively for wavelengths (in metre) of A)  $10,5,\,\frac{5}{2},\,...$                    B)  $20,\,\frac{20}{3},\,\frac{20}{5},\,...$ C)  30, 20, 10, ?             D)  35, 25, 15, ?

As in $\frac{Q}{4\pi {{R}^{2}}}=\frac{q}{4\pi {{r}^{2}}}=\sigma$            $\therefore$ $V=\frac{1}{{{\varepsilon }_{0}}}\,[\sigma R+\sigma r]=\frac{\sigma }{{{\varepsilon }_{0}}}[R+r]$             Path difference ${{N}_{S}}=\left( \frac{\rho S}{\rho P} \right)\times {{N}_{P}}$ $=\frac{(4.4\times {{10}^{3}})\,\times 100}{220}=2000$          ${{\rho }_{S}}$ ${{\rho }_{P}}$        $-h=-u{{t}_{1}}+\frac{1}{2}gt_{1}^{2}$ But at A, the wave suffers reflection at the surface of rigid/fixed end or denser medium, hence the wave must suffer an additional path change of $-h=-u{{t}_{2}}+\frac{1}{2}gt_{2}^{2}$ or a phase change of $0=u({{t}_{2}}-{{t}_{1}})+\frac{1}{2}g(t_{1}^{2}-t_{2}^{2})$. Net path difference $u=\frac{1}{2}g({{t}_{1}}+{{t}_{2}})$ For maximum, net path difference $h=\frac{g{{t}_{1}}{{t}_{2}}}{2}$. $\sqrt{2}\,mv$ $\sqrt{2}\,mv'=(2m)\,v$ or         $\Rightarrow$ $v'\frac{v}{\sqrt{2}}$            $E=\frac{1}{2}mv{{'}^{2}}+\frac{1}{2}mv{{'}^{2}}+\frac{1}{2}(2m){{v}^{2}}$ $=mv{{'}^{2}}+m{{v}^{2}}$   $\Rightarrow$