1. A certain radar installation transmits electromagnetic radiation with a wavelength of 2.5 cm. What is the frequency of this radiation?
2. For the radar above, how many seconds will it take for a signal to reach an airplane 15 km away, and return to the radar installation
To answer these questions, we can use the formula:
Speed of light = frequency × wavelength
1. To find the frequency of the radiation, we can rearrange the formula:
frequency = Speed of light / wavelength
Speed of light is approximately 3 × 10^8 meters per second (m/s), which is 3 × 10^10 centimeters per second (cm/s). Therefore:
frequency = (3 × 10^10 cm/s) / 2.5 cm
frequency = 1.2 × 10^10 Hz
So, the frequency of the radiation is 1.2 × 10^10 Hertz (Hz).
2. To calculate the time it takes for the signal to reach the airplane and return, we need to consider the distance and the speed of the signal. The distance traveled by the signal is twice the distance between the radar and the airplane.
Total distance traveled = 2 × 15 km = 30 km = 30,000 meters
The speed of the signal is the speed of light, which is approximately 3 × 10^8 m/s.
To find the time, we can use the formula:
time = distance / speed
time = (30,000 m) / (3 × 10^8 m/s)
time = 0.1 seconds
Therefore, it will take 0.1 seconds for the signal to reach the airplane and return to the radar installation.
To find the frequency of the electromagnetic radiation transmitted by the radar installation in question 1, you can use the formula:
Frequency (f) = Speed of light (c) / Wavelength (λ)
1. The speed of light in a vacuum is approximately 3 x 10^8 meters per second. However, for a more accurate calculation, let's convert the wavelength from centimeters to meters:
Wavelength (λ) = 2.5 cm = 2.5 x 10^(-2) meters
2. Now, we can substitute the values into the formula:
Frequency (f) = (3 x 10^8) / (2.5 x 10^(-2))
f ≈ 1.2 x 10^10 Hz
So, the frequency of the radiation transmitted by the radar installation is approximately 1.2 x 10^10 Hz.
For question 2, to calculate how many seconds it will take for the signal to reach an airplane 15 km away and return to the radar installation, we need to consider the time taken for the round trip.
The time taken for the signal to travel one way can be found using the formula:
Time (t) = Distance (d) / Speed (s)
1. The distance to the airplane is given as 15 km, which we can convert to meters:
Distance (d) = 15 km = 15,000 meters
2. The speed of light is the appropriate speed to use since electromagnetic radiation travels at the speed of light.
Speed (s) = 3 x 10^8 meters per second
3. Now, we can substitute the values into the formula:
Time (t) = (15,000) / (3 x 10^8)
t ≈ 5 x 10^(-5) seconds
Since this is only the one-way time, to find the total time for the round trip, we multiply it by 2:
Total time = 2 * 5 x 10^(-5) seconds
Total time ≈ 10 x 10^(-5) seconds
So, it will take approximately 10 x 10^(-5) seconds, or 1 x 10^(-4) seconds, for the signal to reach the airplane 15 km away and return to the radar installation.