Physics - Sound Wave Question with Solution | TestHub

Resultant intensity of two periodic waves is given by $I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \delta$ where $\delta$ is the phase difference between the waves. For maximum intensity, $\delta =2n\pi ;n=0,1,2\dots$ etc. Therefore, for zero order maxima, $\cos \delta =1$ $I_{\text{max }}=I_1+I_2+2\sqrt{I_1{I}_2}={\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2$ For minimum intensity, $\delta =(2n-1)\pi$; $n=1,2\dots \text{ etc }$ Therefore, for Ist order minima, $\cos \delta =-1$ $\begin{array}{rl}{I}_{\min }& =I_1+I_2-2\sqrt{I_1{I}_2}\\ & ={\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2\end{array}$ Therefore, $\begin{array}{rl}{I}_{\max }+I_{\min }& ={\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2+{\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2\\ & =2\left(I_1+I_2\right)\end{array}$