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A radar sends a radio signal of frequency 9 x 109 Hz towards an aircraft approaching the radar. If the reflected wave shows a frequency shift of 3 X 103 Hz, the speed with which the aircraft is approaching the radar in m/s is (velocity of radio signal is 3 X 108 m/s).
- a)100
- b)150
- c)50
- d)25
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A radar sends a radio signal of frequency 9 x 109Hz towards an aircraf...
Given:
Frequency of radio signal n=9×10 9Hz
Frequency shift n0=3×103Hz
Velocity of radio signal v=3×108m/s
Frequency shift shown by reflected wave is Shift =n−n
=>n−n=(v+u/v−u)n−n
Shift=(2u/v−u)n
Now, putting the given values in Eq. (i), we get,
3×103=(2u/3×10-8−u)9×109
⇒3×108−u=2u×9×109/3×103
=6u×106
⇒6×106u+u=3×108
u(6×106+1)=3×108
u(6000001)=3×108
u=3×108/6000001=49.999≈50m/s
Frequency of radio signal n=9×10 9Hz
Frequency shift n0=3×103Hz
Velocity of radio signal v=3×108m/s
Frequency shift shown by reflected wave is Shift =n−n
=>n−n=(v+u/v−u)n−n
Shift=(2u/v−u)n
Now, putting the given values in Eq. (i), we get,
3×103=(2u/3×10-8−u)9×109
⇒3×108−u=2u×9×109/3×103
=6u×106
⇒6×106u+u=3×108
u(6×106+1)=3×108
u(6000001)=3×108
u=3×108/6000001=49.999≈50m/s
Most Upvoted Answer
A radar sends a radio signal of frequency 9 x 109Hz towards an aircraf...
Given data:
Frequency of the radar signal, f0 = 9 x 10^9 Hz
Frequency shift, Δf = 3 x 10^3 Hz
Velocity of the radio signal, v = 3 x 10^8 m/s
The Doppler effect is used to determine the velocity of the aircraft. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.
The Doppler formula for frequency shift is given by:
Δf/f0 = v/c
where Δf is the frequency shift, f0 is the original frequency, v is the velocity of the source or observer, and c is the speed of the wave.
In this case, the frequency shift is positive, indicating that the aircraft is approaching the radar. Therefore, the velocity of the aircraft is the negative of the velocity of the radar.
Using the Doppler formula, we can rearrange the equation to solve for v:
v = (Δf/f0) * c
Substituting the given values:
v = (3 x 10^3 Hz) / (9 x 10^9 Hz) * (3 x 10^8 m/s)
v = 1/3 * 10^(-6) * 3 x 10^8 m/s
v = 10^(-6) * 10^8 m/s
v = 10^2 m/s
v = 100 m/s
Therefore, the speed with which the aircraft is approaching the radar is 100 m/s, which corresponds to option C.
Frequency of the radar signal, f0 = 9 x 10^9 Hz
Frequency shift, Δf = 3 x 10^3 Hz
Velocity of the radio signal, v = 3 x 10^8 m/s
The Doppler effect is used to determine the velocity of the aircraft. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.
The Doppler formula for frequency shift is given by:
Δf/f0 = v/c
where Δf is the frequency shift, f0 is the original frequency, v is the velocity of the source or observer, and c is the speed of the wave.
In this case, the frequency shift is positive, indicating that the aircraft is approaching the radar. Therefore, the velocity of the aircraft is the negative of the velocity of the radar.
Using the Doppler formula, we can rearrange the equation to solve for v:
v = (Δf/f0) * c
Substituting the given values:
v = (3 x 10^3 Hz) / (9 x 10^9 Hz) * (3 x 10^8 m/s)
v = 1/3 * 10^(-6) * 3 x 10^8 m/s
v = 10^(-6) * 10^8 m/s
v = 10^2 m/s
v = 100 m/s
Therefore, the speed with which the aircraft is approaching the radar is 100 m/s, which corresponds to option C.
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A radar sends a radio signal of frequency 9 x 109Hz towards an aircraf...
I THINK ANSWER IS 100 CHECK IT OUT ONCE.
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A radar sends a radio signal of frequency 9 x 109Hz towards an aircraft approaching the radar. If the reflected wave shows a frequency shift of 3 X 103Hz, the speed with which the aircraft is approaching the radar in m/s is (velocity of radio signal is 3 X 108 m/s).a)100b)150c)50d)25Correct answer is option 'C'. Can you explain this answer?
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A radar sends a radio signal of frequency 9 x 109Hz towards an aircraft approaching the radar. If the reflected wave shows a frequency shift of 3 X 103Hz, the speed with which the aircraft is approaching the radar in m/s is (velocity of radio signal is 3 X 108 m/s).a)100b)150c)50d)25Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A radar sends a radio signal of frequency 9 x 109Hz towards an aircraft approaching the radar. If the reflected wave shows a frequency shift of 3 X 103Hz, the speed with which the aircraft is approaching the radar in m/s is (velocity of radio signal is 3 X 108 m/s).a)100b)150c)50d)25Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radar sends a radio signal of frequency 9 x 109Hz towards an aircraft approaching the radar. If the reflected wave shows a frequency shift of 3 X 103Hz, the speed with which the aircraft is approaching the radar in m/s is (velocity of radio signal is 3 X 108 m/s).a)100b)150c)50d)25Correct answer is option 'C'. Can you explain this answer?.
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