MCQ
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

  • A
    $(iii, iv), (i, ii)$
  • B
    $(i, iii), (ii, iv)$
  • C
    $(i, iv), (ii, iii)$
  • $(i, ii), (iii, iv)$

Answer

Correct option: D.
$(i, ii), (iii, iv)$
d
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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