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

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:

       

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

       

⇒     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:

       

       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 = 0.2 ms (with two significative figures)