Four identical monochromatic sources $A, B, C, D$ as shown in the figure produce waves of the same wavelength $\lambda$ and are coherent. Two receivers $R_1$ and $R_2$ are at great but equal distances from $B$.
$(i)$ Which of the two receivers picks up the larger signal?
$(ii)$ Which of the two receivers picks up the larger signal when $B$ is turned off?
$(iii)$ Which of the two receivers picks up the larger signal when $D$ is turned off?
$(iv)$ Which of the two receivers can distinguish which of the sources $B$ or $D$ has been turned off?

(B) $(i)$ At $R_1$,the path difference between waves from $A$ and $B$ is $\lambda/2$,leading to destructive interference $(y_A + y_B = 0)$. Similarly,waves from $C$ and $D$ interfere destructively at $R_1$. Thus,the net signal at $R_1$ is zero. At $R_2$,the path differences are different,leading to constructive interference. Therefore,$R_2$ picks up the larger signal.
$(ii)$ If $B$ is turned off,the destructive interference at $R_1$ is removed,resulting in a non-zero signal. $R_2$ also experiences a change,but $R_1$ now receives a stronger resultant signal compared to its previous zero state. Thus,$R_1$ picks up the larger signal.
$(iii)$ If $D$ is turned off,the destructive interference at $R_1$ is removed,resulting in a non-zero signal. $R_1$ picks up the larger signal.
$(iv)$ Since the path differences for $B$ and $D$ are different relative to $R_1$ and $R_2$,the change in signal intensity at the receivers will be unique for each source being turned off. Thus,both receivers can distinguish which source is turned off.