Chapter 22, Problem 27P

(a)

To determine

The range of the wavelength for radio.

Answer to Problem 27P

The range of wavelength is $\text{3}\text{.4}\text{m}-\text{2}\text{.78}\text{m}$ .

Explanation of Solution

Given:

The frequencies are $\text{88 MHz =88000000}\text{Hz}$ and $\text{108}\text{MHz}\text{=}\text{108000000}\text{Hz}$

  $\text{1}\text{MHz}\text{=}\text{1000000}\text{Hz}$

Formula used:

  $\text{λ}\text{=}\frac{\text{c}}{\text{v}}$

  $\text{v}$ is the frequency in $\text{Hz}$ , $\text{c}$ is the speed of light; $\text{c}$ = ${\text{3×10}}^{\text{8}}\text{m/s}$ and $\text{λ}$ is the wavelength.

Calculation:

Substituting the values in the formula $\text{λ}\text{=}\frac{\text{c}}{\text{v}}$

For frequency $\text{88 MHz}$ calculation

  $\text{=}\frac{{\text{3×10}}^{\text{8}}\text{m/s}}{{\text{88×10}}^{\text{6}}\text{Hz}}\text{=}\text{3}\text{.4}\text{m}$

For frequency $\text{108 MHz}$ calculation

  $\text{=}\frac{{\text{3×10}}^{\text{8}}\text{m/s}}{{\text{108×10}}^{\text{6}}\text{Hz}}\text{=}\text{2}\text{.78}\text{m}$

(b)

To determine

The range of wavelength for AM should be determined.

Answer to Problem 27P

The range of wavelength is $\text{561}\text{m}-\text{176}\text{m}$.

Explanation of Solution

Given:

The frequency is $\text{535}\text{MHz}\text{=}\text{5}{\text{.35×10}}^{\text{5}}\text{Hz}$ and $\text{1700}\text{MHz}\text{=1}{\text{.7×10}}^{\text{6}}\text{Hz}$

  $\text{1}\text{KHz}\text{=}\text{1000}\text{Hz}$

Formula used:

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

  $\text{f}$ is Frequency, $\text{c}$ is the speed of light; $\text{c}$ = ${\text{3×10}}^{\text{8}}\text{m/s}$ and $\text{λ}$ is the wavelength.

Calculation:

Substituting the values in the formula $\text{λ=}\frac{\text{c}}{\text{f}}$

Calculation for both frequencies:

= $\frac{{\text{3×10}}^{\text{8}}\text{m/s}}{\text{5}{\text{.35×10}}^{\text{5}}\text{Hz}}\approx 561\text{m}$

  $\text{=}\frac{{\text{3×10}}^{\text{8}}\text{m/s}}{\text{1}{\text{.7×10}}^{\text{6}}\text{Hz}}\approx 176\text{m}$

Conclusion:

The range of wavelength for radio is $\text{561}\text{m}-\text{176}\text{m}$ .