Chapter 24, Problem 63GP

(a)

To determine

The type of interference.

Answer to Problem 63GP

The type of interference is constructive.

Explanation of Solution

Given:

Frequency is $\text{f}\text{=}\text{75}\text{MHz}\text{=}{\text{75×10}}^{\text{6}}\text{Hz}$ ,

Signals reflected from a nearby airplane $\text{118m}$ .

Formula used:

Itis known that $\text{λ=}\frac{\text{c}}{\text{f}}$

Where, $\text{λ}$ is the wavelength, $\text{c}$ speed of light and $\text{f}$ is the frequency.

Calculation:

Calculate the wavelength of the signal by substituting values in formula $\text{λ=}\frac{\text{c}}{\text{f}}$

  $\text{λ=}\frac{\left({\text{3×10}}^{\text{8}}\text{m/s}\right)}{\left({\text{75×10}}^{\text{6}}\text{Hz}\right)}\text{=4}\text{.00}\text{m}$

It is known that there is a phase difference between direct and reflected signals from path difference, $\left(\frac{\text{h}}{\text{λ}}\right)\text{2π}$ and reflection is $\text{π}$

Now, calculate the phase difference is $\varphi \text{=}\left(\frac{\text{h}}{\text{λ}}\right)\text{2π}\text{+}\text{π =}\left[\frac{\left(\text{118}\text{m}\right)}{\text{4}\text{.00}\text{m}}\right]\text{2π + π = 30}\left(\text{2π}\right)$

Hence, the interference is constructive.

(b)

To determine

The type of interference.

Answer to Problem 63GP

The type of interference is destructive.

Explanation of Solution

Given:

Signals reflected from a nearby airplane $\text{118m}$ .

The plane is $\text{22}\text{m}$ closer to receiver.

Formula used:

Itis known that $\text{λ=}\frac{\text{c}}{\text{f}}$

Where, $\text{λ}$ is the wavelength, $\text{c}$ speed of light and $\text{f}$ is the frequency.

Calculation:

Calculate the wavelength of the signal by substituting values in formula $\text{λ=}\frac{\text{c}}{\text{f}}$

  $\text{λ=}\frac{\left({\text{3×10}}^{\text{8}}\text{m/s}\right)}{\left({\text{75×10}}^{\text{6}}\text{Hz}\right)}\text{=4}\text{.00}\text{m}$

When the plane is $\text{22}\text{m}$ closer to the receiver. So, the phase difference is

  $\varphi \text{=}\left(\frac{\text{h-y}}{\text{λ}}\right)\text{2π}\text{+}\text{π =}\left[\frac{\left(\text{118}\text{m}\text{-}\text{22}\text{m}\right)}{\text{4}\text{.00}\text{m}}\right]\text{2π + π =24}\left(\text{2π}\right)+\pi$

Hence, the interference is destructive.