9. A certain radar installation transmits electromagnetic radiation with a wavelength of 2.5 cm. What is the frequency of this radiation?
10. For the radar in #9 above, how many seconds will it take for a signal to reach an airplane 15 km away, and return to the radar installation?
To find the frequency of electromagnetic radiation, we can use the formula:
Speed of light (c) = wavelength (λ) * frequency (f)
We know the wavelength (λ) is given as 2.5 cm. The speed of light (c) is a constant value, approximately equal to 3 x 10^8 meters per second.
Step 1: Convert the wavelength from cm to meters:
2.5 cm = 2.5 / 100 meters = 0.025 meters (since 1 meter = 100 centimeters)
Step 2: Rearrange the formula to solve for frequency (f):
f = c / λ
Step 3: Substitute the values:
f = (3 x 10^8 m/s) / 0.025 m
Step 4: Calculate the frequency (f):
f = 1.2 x 10^10 Hz
Therefore, the frequency of the radiation is approximately 1.2 x 10^10 Hz.
Now, moving on to question 10, to find the time it takes for the signal to reach the airplane and return to the radar installation, we can use the formula:
Time = Distance / Speed
We are given the distance as 15 km, which needs to be converted to meters (1 km = 1000 meters) before we can calculate the time. Also, the speed of light (c) is again used as a constant value.
Step 1: Convert the distance from km to meters:
15 km = 15 x 1000 meters = 15000 meters
Step 2: Calculate the time:
Time = Distance / Speed
Time = 15000 meters / (3 x 10^8 m/s)
Step 3: Calculate the time:
Time = 5 x 10^-5 seconds
or
Time = 50 microseconds
Therefore, it will take approximately 50 microseconds for the signal to reach the airplane 15 km away and return to the radar installation.