91Ó°ÊÓ

Intensity is given by

$\mathit{I}\mathbf{=}{\mathit{I}}_{\mathbf{0}}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\left(\frac{\mathrm{Ï•}}{2}\right)$ (1)

Phase difference is given by

$\mathit{ϕ}\mathbf{=}\frac{\mathbf{∆}\mathbf{r}\mathbf{*}\mathbf{2}\mathbf{π}}{\mathbf{λ}}$ (2)

Given:

d = 9.0m

$\mathit{f}\mathbf{=}\mathbf{120}\mathit{M}\mathit{H}\mathit{z}\mathbf{=}\mathbf{120}\mathbf{*}{\mathbf{10}}^{\mathbf{6}}\mathit{H}\mathit{z}$

$$\begin{gathered} {\mathit{r}}_{\mathbf{1}}\mathbf{=}{\mathit{r}}_{\mathbf{2}}\mathbf{=}\mathbf{150}\mathit{m} \\ \mathbf{∆}{\mathit{r}}_{\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{8}\mathit{m} \end{gathered}$$

The speed of electromagnetic waves is as same as the speed of light. So, the speed of wave emitted from both stations is given by

$\mathit{c}\mathbf{=}\mathit{λ}\mathit{f}\mathbf{⇒}\mathit{λ}\mathbf{=}\frac{\mathbf{c}}{\mathbf{f}}$ (3)

In equation (2), plug equation (3),

$\mathit{ϕ}\mathbf{=}\frac{\mathbf{2}\mathbf{π}\mathbf{f}\mathbf{∆}\mathbf{r}}{\mathbf{c}}$ (4)

When the receiver is moved closer to one antenna than to the other,

Plug the given in equation (4),

$\mathit{Ï•}\mathbf{=}\frac{\mathbf{2}\mathbf{Ï€}\mathbf{*}\mathbf{120}\mathbf{*}{\mathbf{10}}^{\mathbf{6}}\mathbf{*}\mathbf{1}\mathbf{.}\mathbf{80}}{\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{*}{\mathbf{10}}^{\mathbf{8}}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{52}\mathit{r}\mathit{a}\mathit{d}$

From equation (1), plug the given

$\mathit{I}\mathbf{=}{\mathit{I}}_{\mathbf{0}}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathbf{\left(}\frac{\mathbf{4}\mathbf{.}\mathbf{52}}{\mathbf{2}}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{404}{\mathit{I}}_{\mathbf{0}}$

Thus, the phase difference$\mathit{Ï•}$ between the two radio waves produced by this path difference is 4.52rad. The intensity measured by the receiver at its new position is $\mathbf{0}\mathbf{.}\mathbf{404}{\mathit{I}}_{\mathbf{0}}$.