MCQ
Two waves represented by $\text{y}=\text{a}\sin(\omega\text{t}-\text{kx})$ and $\text{y}=\text{a}\cos(\omega\text{t}-\text{kx})$ are superposed. The resultant wave will have an amplitude:
- Aa
- ✓$\sqrt{2}\text{a}$
- C2a
- D0.
✓
Answer
Correct option: B.
$\sqrt{2}\text{a}$
Explanation:
We know that the resultant of the amplitude is given by
$\text{R}_\text{net}=\sqrt{\text{A}_1^2+\text{A}_2^2+2\text{A}_1\text{A}_2\cos\phi}$
For the particular case, we can write
$=\sqrt{\text{a}^2+\text{a}^2+2\text{a}^2\cos\frac{\pi}{2}}$
$=\sqrt{2}\text{a}$
We know that the resultant of the amplitude is given by
$\text{R}_\text{net}=\sqrt{\text{A}_1^2+\text{A}_2^2+2\text{A}_1\text{A}_2\cos\phi}$
For the particular case, we can write
$=\sqrt{\text{a}^2+\text{a}^2+2\text{a}^2\cos\frac{\pi}{2}}$
$=\sqrt{2}\text{a}$
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