Question

Two waves represented by $y\, =\, asin(\omega\,t - kx)$ and $y \,= \,acos(\omega\,t - kx)$ are superposed. The resultant wave will have an amplitude

• A. a
• B. $\sqrt{2a}$
• C. 2a
• D. zero

Answer 1

Answer: (B)

$\sqrt{2a}$

Answer 2

Given, $\quad$y = asin(?t - kx) and y = a cos(?t - kx) Here, the phase difference between the two waves is $\frac{\pi}{2}$. So, the resultant amplitude, $A=\sqrt{a_{1}^{2}+a_{_2}^{2}+2a_{1}a_{2} cos \phi}$ Here$a1 = a, a2 = a, \phi=\frac{\pi}{2}$ $\therefore\quad A=\sqrt{a^{2}+a^{2}+2a^{2} cos \frac{\pi}{2}}$ or$\quad A=\sqrt{a^{2}+a^{2}+0}\Rightarrow A=\sqrt{2}a$