Question

A radio transmitting station operating at a frequency of $120$MHz has two identical antennas that radiate in phase. Antenna $B$ is $9m$ to the right of antenna $A$. Consider point $P$ at a horizontal distance $x$ to the right of antenna $A$ as shown figure. The value of $x$ and order for which the constructive interference will occur at point $P$ are

• A. $x=14.95m,n=1$
• B. $x=5.6m,n=2$
• C. $x=1.65m,n=3$
• D. $x=0,n=3.6$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $x=14.95m,n=1$
B $x=5.6m,n=2$
C $x=1.65m,n=3$

For constructive interference at point P, the path difference between the radio signals at point P=$n\lambda$

$⟹\sqrt{x^2+{81}^2}-x=n\lambda$,....... Equation 1

$\lambda =\frac{c}{\nu }=\frac{3\times {10}^8}{120\times {10}^6}=2.5m$

Using equation 1,

For n=1, $x=14.95m$

For n=2, $x=5.6m$

For n=3, $x=1.65m$

n can have integer values only. Hence option D is not possible.