The path difference between the two waves $y_{1} = a_{1} \sin \left( \omega t - \frac{2 \pi x}{\lambda} \right)$ and $y_2 = a_2 \cos \left( \omega t - \frac{2 \pi x}{\lambda} + \varphi \right)$ is
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$y_{1} = a_{1} \sin \left( \omega t - \frac{2 \pi x}{\lambda} \right)$ and
$y_{2} = a_{2} \cos \left( \omega t - \frac{2 \pi x}{\lambda} + \varphi \right) = a_{2} \sin \left( \omega t - \frac{2 \pi x}{\lambda} + \varphi + \frac{\pi}{2} \right)$
So phase difference $=\varphi + \frac{\pi}{2}$ and Δ Δ = $\frac{\lambda}{2 \pi} \left( \varphi + \frac{\pi}{2} \right)$
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