A radar antenna emits electromagnetic radiation of velocity 3×10^8 m/s with a wavelength of 0.03 for 0.5 seconds.
a) what is the frequency of the radiation
b) how many complete waves are emitted in this time
c) after 0.5 seconds how far is the front of the wave from the antenna
a) To find the frequency of the radiation, we can use the formula:
frequency = speed of light / wavelength
The speed of light is given as 3×10^8 m/s, and the wavelength is given as 0.03 m. Plugging these values into the formula, we get:
frequency = (3×10^8 m/s) / (0.03 m)
frequency = 1×10^10 Hz
Therefore, the frequency of the radiation is 1×10^10 Hz.
b) To find the number of complete waves emitted in 0.5 seconds, we can use the formula:
number of waves = frequency * time
The frequency is given as 1×10^10 Hz, and the time is given as 0.5 seconds. Plugging these values into the formula, we get:
number of waves = (1×10^10 Hz) * (0.5 s)
number of waves = 5×10^9 waves
Therefore, the number of complete waves emitted in 0.5 seconds is 5×10^9.
c) The distance traveled by the front of the wave after 0.5 seconds can be calculated using the formula:
distance = speed of light * time
The speed of light is given as 3×10^8 m/s, and the time is given as 0.5 seconds. Plugging these values into the formula, we get:
distance = (3×10^8 m/s) * (0.5 s)
distance = 1.5×10^8 m
Therefore, after 0.5 seconds, the front of the wave is 1.5×10^8 meters away from the antenna.
Let's break down each part of the question step-by-step:
a) To find the frequency of the radiation, we can apply the formula:
frequency = wave velocity / wavelength
Given:
wave velocity = 3 × 10^8 m/s
wavelength = 0.03 m
Substituting these values into the formula:
frequency = (3 × 10^8 m/s) / (0.03 m)
Calculating:
frequency = 10^10 Hz
Therefore, the frequency of the radiation is 10^10 Hz.
b) To determine the number of complete waves emitted in 0.5 seconds, we need to calculate the period of one wave:
period = 1 / frequency
Given:
frequency = 10^10 Hz
Substituting this value into the formula:
period = 1 / (10^10 Hz)
Calculating:
period = 10^-10 s
Since the antenna emits waves for 0.5 seconds, we can find the number of waves emitted by dividing the time by the period:
number of waves = time / period
Given:
time = 0.5 seconds
Substituting these values into the formula:
number of waves = 0.5 s / (10^-10 s)
Calculating:
number of waves = 5 × 10^9 waves
Therefore, the antenna emits 5 × 10^9 complete waves in 0.5 seconds.
c) After 0.5 seconds, the distance the front of the wave has traveled can be found by multiplying the wave velocity by time:
distance = wave velocity × time
Given:
wave velocity = 3 × 10^8 m/s
time = 0.5 seconds
Substituting these values into the formula:
distance = (3 × 10^8 m/s) × (0.5 seconds)
Calculating:
distance = 1.5 × 10^8 meters
Therefore, after 0.5 seconds, the front of the wave is 1.5 × 10^8 meters away from the antenna.
To solve this problem, we need to understand the relationship between wavelength, frequency, and velocity of electromagnetic radiation.
a) The frequency (f) of electromagnetic radiation is given by the equation:
f = velocity / wavelength
Plugging in the given values:
velocity = 3x10^8 m/s
wavelength = 0.03 m
f = (3x10^8 m/s) / (0.03 m)
= 1x10^10 Hz
The frequency of the radiation is 1x10^10 Hz.
b) To find the number of complete waves emitted in 0.5 seconds, we need to calculate the period (T) of the wave.
The period is the time taken for one complete wave. It is the inverse of frequency:
T = 1 / f
Plugging in the given value of frequency (1x10^10 Hz):
T = 1 / (1x10^10 Hz)
= 1x10^-10 s
Next, we divide the total time (0.5 s) by the period (T):
Number of complete waves = Total time / Period
= 0.5 s / 1x10^-10 s
= 5x10^9 waves
Therefore, 5x10^9 complete waves are emitted in 0.5 seconds.
c) To find how far the front of the wave is from the antenna after 0.5 seconds, we use the formula:
Distance = velocity x time
Plugging in the given values:
Distance = (3x10^8 m/s) x (0.5 s)
= 1.5x10^8 m
Therefore, the front of the wave is 1.5x10^8 meters away from the antenna after 0.5 seconds.