Physics - Sound Wave Question with Solution | TestHub

Given that, two waves

$y=a\sin \left(\omega t-ka\right)$

And$y=a \cos (\omega t-kx)$

Here, the phase difference between the two waves is$\frac{\pi }{2}$.

So, the resultant amplitude

$A=\sqrt{a_1^2+a_2^2+2a_1{a}_2\cos \mathrm{\Phi }}$

$\left(Here a_1=a,a_2=a,\mathrm{\Phi }=\frac{\mathrm{\pi }}{2}\right)$

$\therefore \mathrm{A}=\sqrt{{\mathrm{a}}^2+{\mathrm{a}}^2+2\mathrm{a}\mathrm{ }\mathrm{a}\cos \frac{\mathrm{\pi }}{2}}\mathrm{ }$

$\mathrm{o}\mathrm{r}\mathrm{ }\mathrm{ }\mathrm{A}=\sqrt{{\mathrm{a}}^2+{\mathrm{a}}^2+0}$

$⟹\mathrm{A}=\sqrt{2}\mathrm{a}$