Question

Telephone signals are often transmitted over long distances by microwaves. What is the frequency of microwave radiation with a wavelength of 3.5 cm?
Express your answer in GHz and using two significant figures.
f = ________GHz
Microwave signals are beamed between two mountaintops 52 km apart. How long does it take a signal to travel from one mountaintop to the other?
Express your answer in ms and using two significant figures.
t = ________ms

Answer 1

Answer:

1) f= 8.6 GHz

2) t= 0.2 ms

Explanation:

1)

• Since microwaves are electromagnetic waves, they move at the same speed as the light in vacuum, i.e. 3*10⁸ m/s.
• There exists a fixed relationship between the frequency (f) , the wavelength (λ) and the propagation speed in any wave, as follows:

        $v = \lambda * f (1)$

• Replacing by the givens, and solving for f, we get:

       $f =\frac{c}{\lambda} =\frac{3e8m/s}{0.035m} = 8.57e9 Hz (2)$

⇒     f = 8.6 Ghz (with two significative figures)

2)

• Assuming that the microwaves travel at a constant speed in a straight line (behaving like rays) , we can apply the definition of average velocity, as follows:

       $v =\frac{d}{t} (3)$

       where v= c= speed of light in vacuum = 3*10⁸ m/s

       d= distance between mountaintops = 52 km = 52*10³ m

• Solving for t, we get:

       $t = \frac{d}{c} = \frac{52e3m}{3e8m/s} = 17.3e-5 sec = 0.173e-3 sec = 0.173 ms (4)$

       ⇒  t = 0.2 ms (with two significative figures)