Q103 / 180 · AIIMS 2014 · Physics
Two waves represented by $y=a \sin (\omega t-k x)$ and $y=a \cos (\omega t-k x)$ are superposed. The resultant wave will have an amplitude
- A$a$
- Correct answerB$\sqrt{2} a$
- C$2 a$
- Dzero
Solution
Given,$y=a \sin (\omega t-k x) \text { and } y=a \cos (\omega t-k x)$
Here, the phase difference between the two waves is $\frac{\pi}{2}$.
So, the resultant amplitude,
$A=\sqrt{a_1^2+a_2^2+2 a_1 a_2 \cos \phi}$
Here $a_1=a, a_2=a, \phi=\frac{\pi}{2}$
$\therefore \quad A=\sqrt{a^2+a^2+2 a^2 \cos \frac{\pi}{2}}$
or $\quad A=\sqrt{a^2+a^2+0} \Rightarrow A=\sqrt{2} a$
Hence, the correct answer is option: 'B'.