Physics - SHM Question with Solution | TestHub

Given,$y=a\sin (\omega t-kx)\text{ and }y=a\cos (\omega t-kx)$ Here, the phase difference between the two waves is $\frac{\pi }{2}$. So, the resultant amplitude, $A=\sqrt{a_1^2+a_2^2+2a_1{a}_2\cos \varphi }$ Here $a_1=a,a_2=a,\varphi =\frac{\pi }{2}$ $\therefore A=\sqrt{a^2+a^2+2a^2\cos \frac{\pi }{2}}$ or $A=\sqrt{a^2+a^2+0}\Rightarrow A=\sqrt{2}a$