A radar installation that is used to track airplanes transmits electromagnetic radiation with a wavelength of 4 cm. Calculate the frequency of this radiation in Hz.
Calculate the time required for a pulse of radar waves to reach an airplane 4.0 km away and return.
λ=c/f,
f=c/λ=3•10^8/0.04 =7.5•10^9 Hz.
s=v•t
t=s/v=s/c= 4000/3•10^8 =1.33•10^-5 s.
To calculate the frequency of the electromagnetic radiation, you can use the formula:
Frequency (f) = Speed of Light (c) / Wavelength (λ)
Since the question provides the wavelength as 4 cm, we need to convert it to meters by dividing by 100:
λ = 4 cm / 100 = 0.04 m
The speed of light is a constant value, which is approximately 3 × 10^8 m/s.
Now, we can substitute the values into the formula:
f = (3 × 10^8 m/s) / (0.04 m) = 7.5 × 10^9 Hz
Therefore, the frequency of the electromagnetic radiation is approximately 7.5 × 10^9 Hz.
To calculate the time required for the radar wave to reach an airplane 4.0 km away and return, we need to consider the round-trip distance.
The distance to the airplane is 4.0 km, which is equal to 4,000 meters. Since the wave needs to travel this distance twice (to reach the airplane and then return), the round-trip distance is:
Total distance = 4,000 m + 4,000 m = 8,000 m
Now, we can use the speed of light to calculate the time:
Time = Distance / Speed = 8,000 m / (3 × 10^8 m/s)
Time = 2.67 × 10^-5 seconds
Therefore, it takes approximately 2.67 × 10^-5 seconds for a pulse of radar waves to reach an airplane 4.0 km away and return.