Question

Following are expressions for four plane simple harmonic waves
(i) $y_1=Acos2\pi \left(n_{1}t+\frac{x}{{\lambda }_1}\right)$
(ii) $y_2=Acos2\pi \left(n_{1}t+\frac{x}{{\lambda }_1}+\pi \right)$
(iii) $y_3=Acos2\pi \left(n_{1}t+\frac{x}{{\lambda }_2}\right)$
(iv) $y_4=Acos2\pi \left(n_{1}t+\frac{x}{{\lambda }_2}\right)$
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 $\varphi =180^{°}$ 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.