The path difference between the two waves $y_{1} = a_{1} \sin (ωt - \frac{2 πx}{λ}) and y_{2} = a_{2} \cos (ωt - \frac{2 πx}{λ} + ϕ) is$

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$\frac{λ}{2 π} (ϕ + \frac{π}{2})$

$\frac{2 π}{λ} (ϕ)$

$\frac{λ}{2 π} ϕ$

$\frac{2 π}{λ} (ϕ - \frac{π}{2})$

answer is B.

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Detailed Solution

$\begin{array}{l} y_{1} = a_{1} \sin (ωt - \frac{2 πx}{λ}) \\ y_{2} = a_{2} \sin (ωt - \frac{2 πx}{λ} + ϕ + \frac{π}{2}) \end{array}$

Phase difference

$= (ωt - \frac{2 πx}{λ} + ϕ + \frac{π}{2}) - (ωt - \frac{2 πx}{λ}) = (ϕ + \frac{π}{2})$

$Path difference = \frac{λ}{2 π} \times Phase difference = \frac{λ}{2 π} (ϕ + \frac{π}{2})$

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