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A certain radar installation tracks airplanes by transmitting electromagnetic radiation of wavelength 4.0 cm.

a)Find the frequency of this radiation. b)Find the time required for a pulse of radar waves to reach an airplane 4.8 km away and return.

Verified Answer :

MissPhiladelphia

the wavelength equation is

speed (of light in this
case)= wavelength (m) x frequency

3x10^8m/s / .07m = f

frequency= 4 285 714 286
hertz

 

 

 

b) Total distance= 4.8 km
(4,800 m)

Speed = 3x10^8 m/s

d=st

t= d/s

t= 4,800 m/3x10^8m/s

t= 1x10^-5 seconds

Answer:

a) frequency = \(7.5 \times 10^9 hz\)

b) times = \(3.2 \times 10^{-5} s\)

Explanation:

Part a)

As we know that frequency of radiation is given as

\(frequency = \frac{speed}{wavelength}\)

now we know that

\(speed = 3 \times 10^8 m/s\)

\(wavelength = 4 cm\)

now frequency is given as

\(f = \frac{3 \times 10^8}{4 \times 10^{-2}}\)

\(f = 7.5 \times 10^9 Hz\)

Part b)

Time required for the pulse to reach the airplane and return is given by formula

\(t = \frac{distance}{speed}\)

total distance for moving to and fro = 4.8 km + 4.8 km = 9.6 km

speed of the wave = \(3 \times 10^8 m/s\)

now times is given as

\(t = \frac{9.6 \times 10^3}{3 \times 10^8}\)

\(t = 3.2 \times 10^{-5} s\)

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