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.

λ= c/f =>

f = c/ λ =3•10^8/4•10^-2 =7.5•10^-9 Hz,
t =2•s/c =2•4800/3•10^8=3.2•10^-5 s.

a) Well, if the wavelength is 4.0 cm, then we can find the frequency by using the formula: frequency = speed of light / wavelength. The speed of light is approximately 3.00 x 10^8 m/s or, if you prefer, 3.00 x 10^10 cm/s, since there are 100 centimeters in a meter. Plugging in the values, we get: frequency = (3.00 x 10^10 cm/s) / 4.0 cm. Go ahead, divide and conquer!

b) Ah, the time it takes for a pulse to travel to the airplane and back. To find that, we need to use the formula: time = distance / speed. The distance is given as 4.8 km, which is 4800 m, and the speed of light is 3.00 x 10^8 m/s. Plug in the values and calculate your way to an answer!

To find the frequency of the radiation, we can use the formula:

frequency = speed of light / wavelength

a) The speed of light is approximately 3.0 x 10^8 meters per second.

First, we need to convert the wavelength to meters:
1 cm = 0.01 m

So, the wavelength is 4.0 cm = 0.04 m.

Now, we can calculate the frequency:

frequency = speed of light / wavelength
frequency = (3.0 x 10^8 m/s) / (0.04 m)
frequency = 7.5 x 10^9 Hz

Therefore, the frequency of the radiation is 7.5 x 10^9 Hz.

b) To find the time required for a pulse of radar waves to reach an airplane 4.8 km away and return, we need to calculate the round trip distance and divide it by the speed of light.

The round trip distance is 2 times the distance to the airplane, as the pulse needs to travel to the airplane and then back.

Distance to the airplane = 4.8 km = 4800 m

Round trip distance = 2 * distance to the airplane
Round trip distance = 2 * 4800 m
Round trip distance = 9600 m

Now, we can calculate the time required:

time = round trip distance / speed of light
time = 9600 m / (3.0 x 10^8 m/s)
time = 3.2 x 10^-5 seconds

Therefore, the time required for a pulse of radar waves to reach an airplane 4.8 km away and return is 3.2 x 10^-5 seconds.

To find the frequency of the radar waves, we can use the formula:

Frequency = Speed of Light / Wavelength.

a) Find the frequency of the radar waves:
The speed of light is approximately 3.00 x 10^8 m/s. However, the wavelength is given in centimeters, so we need to convert it to meters by multiplying by 0.01.

Wavelength = 4.0 cm x 0.01 m/cm = 0.04 m

Frequency = (3.00 x 10^8 m/s) / (0.04 m)
Frequency ≈ 7.50 x 10^9 Hz

So the frequency of the radar waves is approximately 7.50 x 10^9 Hz.

b) To find the time required for a pulse of radar waves to reach an airplane 4.8 km away and return, we need to consider the round-trip distance and the speed of light.

The round-trip distance is 2 times the distance of 4.8 km:
Round-trip distance = 2 * 4.8 km

First, convert 4.8 km to meters by multiplying by 1000:
Round-trip distance = 2 * 4.8 km * 1000 m/km = 9,600 meters.

Next, we need to calculate the time using the equation: Time = Distance / Speed.

Time = (9,600 meters) / (3.00 x 10^8 m/s)
Time ≈ 3.2 x 10^-5 seconds.

So the time required for a pulse of radar waves to reach an airplane 4.8 km away and return is approximately 3.2 x 10^-5 seconds.