Question

Two waves represented by $y=a\sin \left(\omega t-kx\right)$ and $y=a\cos \left(\omega t-kx\right)$ are superposed. The resultant wave will have an amplitude
(a) a
(b) $\sqrt{2}a$
(c) 2a
(d) 0.

Answer 1

(b) $\sqrt{2}a$

We know that the resultant of the amplitude is given by
$R_{\mathrm{net}}=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \varphi }$
For the particular case, we can write
$$\begin{gathered} =\sqrt{a^2+a^2+2a^2\cos \frac{\mathrm{\pi }}{2}} \\ =\sqrt{2}a \end{gathered}$$