Question

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) $y_3=A\,cos\,2\pi\left(n_{1}t +\frac{x}{\lambda_{2}}\right)$
(iv) $y_{4}=A\,cos\,2\pi\left(n_{1}t +\frac{x}{\lambda_2}\right)$
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. $(i, iv), (ii, iii)$
• D. $(i, ii), (iii, iv)$

Answer 1

Answer: (D)

In case of destructive interference Phase difference $\phi = 180^°$ or $\pi$
So wave pair (i) and (ii) will produce destructive interference.
Stationary or standing waves will produce by equations (iii) & (iv) as two waves travelling along the same line but in opposite direction.