Question

A radio transmitter at position $A$ operates at a wavelength of 20 m. A second , identical transmitter is located at a distance $x$ from the first transmitter , at position $B$. The transmitters are phase locked together such that the second transmitter is lagging $\pi /2$ out of phase with the first. For which of the following values of $BC-CA$ will the intensity at $C$ be maximum?

• A. 60 m
• B. 65 m
• C. 55 m
• D. 75 m

Answer 1

Answer: (C), (D)

The correct options are
C 55 m
D 75 m

$y_A=Asin[\omega t-k(AC\left)\right]$
$y_B=Asin[\omega t-(\pi \left)/\right(2)-k(BC\left)\right]$
For maximum intensity at C,
$k(BC-AC)+\frac{\pi }{2}=2n\pi$
$BC-AC=(n\lambda -(\lambda \left)/\right(4\left)\right)=15,35,55,75,\dots .$