Waves

JEE Main level, single correct, medium

57 of 142

Question 57 of 142

Following are expressions for four plane simple harmonic waves
(i)
y1=Acos⁡2π(n1t+xλ1)\quad y_1=A \cos 2 \pi\left(n_1 t+\frac{x}{\lambda_1}\right)
(ii)
y2=Acos⁡2π(n1t+xλ1+π)y_2=A \cos 2 \pi\left(n_1 t+\frac{x}{\lambda_1}+\pi\right)
(iii)
y3=Acos⁡2π(n2t+xλ2)y_3=A \cos 2 \pi\left(n_2 t+\frac{x}{\lambda_2}\right)
(iv)
y4=Acos⁡2π(n2t−xλ2)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

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Answer: (D) (i, ii), (iii, iv)

In case of destructive interference Phase difference ϕ=180∘\phi=180^{\circ} or π\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.

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