Question

the path difference between two waves $y_1=A_1\sin \omega t$ and $y_2=A_2\cos (\omega t+\varphi )$ will be

• A. $\left(\lambda /2\pi \right)\varphi$
• B. $\left(\lambda /2\pi \right)(\varphi +\pi /2)$
• C. $\left(2\pi /\lambda \right)(\varphi -\pi /2)$
• D. $\left(2\pi /2\right)\varphi$

Answer 1

The correct option is C $\left(2\pi /\lambda \right)(\varphi -\pi /2)$

Given,

$y_1=A_1\sin \omega t$

And, $y_2=A_2\cos [90+(\omega t+\varphi -90\left)\right]=A_2\sin (\omega t+\varphi -90)$

So, Phase Difference = $\varphi -\frac{\pi }{2}$

And path difference $=\frac{2\pi }{\lambda }$ $(\varphi -\frac{\pi }{2})$

Therefore, C is correct option