A certain radar installation used to track airplanes transmits electromagnetic radiation of wavelength 7 cm.
(a) What is the frequency of this radiation, measured in billions of hertz (GHz)? __________GHz
(b) What is the time required for a pulse of radar waves to reach an airplane 3 km away and return? ________s
a) use the wave equation
frequency*wavelength=speed of light
b) time= 2*3km/speedlght
What is the time required for a pulse of radar waves to reach an airplane 7 km away and return?
To find the frequency of the radar waves transmitted by the radar installation, we can use the formula:
c = λ * f
where c is the speed of light (approximately 3 * 10^8 m/s), λ is the wavelength, and f is the frequency.
(a) To find the frequency in GHz, we need to convert the wavelength from centimeters to meters:
wavelength = 7 cm = 7 * 10^-2 m
Now we can rearrange the formula for frequency:
f = c / λ
f = (3 * 10^8 m/s) / (7 * 10^-2 m)
f ≈ 4.29 * 10^9 Hz
Converting to GHz:
f ≈ 4.29 GHz
Therefore, the frequency of the radar waves is approximately 4.29 GHz.
(b) To find the time required for a pulse of radar waves to reach the airplane 3 km away and return, we can use the formula:
time = (2 * distance) / speed
where distance is the roundtrip distance covered by the radar waves (3 km = 3000 m), and speed is the speed of light (approximately 3 * 10^8 m/s).
time = (2 * 3000 m) / (3 * 10^8 m/s)
time = 2 * 10^-2 s
Therefore, the time required for a pulse of radar waves to reach the airplane 3 km away and return is 0.02 seconds.
To answer these questions, we need to use the relationship between the wavelength, frequency, and speed of electromagnetic radiation.
(a) To find the frequency of the radiation, we can use the equation:
Frequency = Speed of light / Wavelength
The speed of light in a vacuum is approximately 3 x 10^8 meters per second (m/s), which is equivalent to 300,000,000 m/s.
First, we need to convert the wavelength to meters. Since 1 meter is equal to 100 centimeters, we divide 7 cm by 100 to get the wavelength in meters:
Wavelength = 7 cm / 100 = 0.07 m
Now, we can substitute the values into the equation:
Frequency = 300,000,000 m/s / 0.07 m = 4,285,714,285.71 Hz
To convert this frequency to gigahertz (GHz), we divide by 1,000,000,000:
Frequency = 4,285,714,285.71 Hz / 1,000,000,000 = 4.2857 GHz
So, the frequency of the radiation is approximately 4.2857 GHz.
(b) To find the time required for a pulse of radar waves to reach an airplane 3 km away and return, we need to calculate the total distance traveled and then divide it by the speed of light.
The pulse travels from the radar installation to the airplane, covering a distance of 3 km (which is equivalent to 3000 meters), and then returns another 3 km.
Total distance traveled = 3000 meters (one way) + 3000 meters (return) = 6000 meters
Now, we can calculate the time required using the equation:
Time = Distance / Speed
Substituting the values:
Time = 6000 meters / 300,000,000 m/s = 0.00002 s
Therefore, the time required for a pulse of radar waves to reach an airplane 3 km away and return is 0.00002 seconds, or 2 x 10^-5 seconds.