Following are expressions for four plane simple harmonic waves
$(i)\,\,\,\,\,{y_1} = A\,\cos \,\,2\pi \,\left( {{n_1}t\, + \,\frac{x}{{{\lambda _1}}}} \right)$
$(ii)\,\,\,\,\,{y_2} = A\,\cos \,\,2\pi \,\left( {{n_1}t\, + \,\frac{x}{{{\lambda _1}}} + \pi } \right)$
$(iii)\,\,\,\,\,{y_3} = A\,\cos \,\,2\pi \,\left( {{n_2}t\, + \,\frac{x}{{{\lambda _2}}}} \right)$
$(iv)\,\,\,\,\,{y_4} = A\,\cos \,\,2\pi \,\left( {{n_2}t\, - \,\frac{x}{{{\lambda _2}}}} \right)$
The pairs of waves which will produce destructive interference and stationary waves respectively in a medium, are
AIEEE 2012, Medium
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In case of destructive interference Phase difference $\phi = 180^o$ or $\pi $ So wave pair $(i)$ and $(ii)$ will produce destructive interference. Stationary or standing waves will produce by equations $(iii)$ and $(iv)$ as two waves travelling along the same line but in opposite direction
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