Question

Which of the following two wave equations can form stationary wave?

(i) $Y=Asin(\omega t-kx)$

(ii) $Y=Acos(\omega t-kx)$

(iii) $Y=Asin(\omega t+kx)$

(iv) $Y=Acos(\omega t+kx)$

• A. $\left(i\right)$ and $\left(ii\right)$
• B. $\left(iii\right)$ and $\left(iv\right)$
• C. $\left(i\right)$ and $\left(iv\right)$
• D. Both $\left(1\right)$ and $\left(2\right)$

Answer 1

Answer: (B), (D)

Both $\left(A\right)$ and $\left(B\right)$.

The necessary condition to form stationary waves is :
Same waves travelling in opposite directions must superimpose.
Hence (i) and iii make a pair of the same waves travelling in opposite directions.

Also (ii) and (iv) make another pair of the same waves travelling in opposite directions.
Hence option (D) is correct.