Question

Consider that the radar, looking in the y-direction (vertical direction), is located at the origin (x, = 0, y = 0), and the target at the initial position (2= -10, yr = 20) Km moves at a constant velocity of 10m/sec in the x-direction (horizontal direction) and reaches the new position at (2n = 20, yr = 20) Km after some time. When the target is at the position (2, = 0, yr = 20) Km, it will be straight above the radar. The radar operating frequency is 5 GHz.

Calculate the Doppler frequency when the target is at the initial position (xp = -10, yr = 20) Km.

Answer 1

To calculate the Doppler frequency at the target's initial position, we use the Doppler effect formula. However, there will be no Doppler shift observed because the target's motion is perpendicular to the radar's line of sight. The observed frequency will remain at 5 GHz, the same as the emitted frequency.

Step-by-step explanation:

Calculating the Doppler Frequency

To calculate the Doppler frequency when the target is at its initial position of (-10 km, 20 km), we must consider the relative velocity between the radar and the target. Since the target moves at 10 m/s in the x-direction and the radar frequency is 5 GHz, we can use the formula for the Doppler effect to find the frequency shift.

The Doppler effect formula is: f' = f (c + vr) / (c + vs), where f' is the observed frequency, f is the emitted frequency, vr is the velocity of the receiver relative to the medium, and vs is the velocity of the source relative to the medium.

In this case, the receiver (radar) is stationary (vr = 0), and the source (target) moves horizontally with a velocity of vs = 10 m/s towards the positive x-direction. However, because the motion is perpendicular to the line of sight, there is no Doppler shift.

Therefore, since there is no velocity component of the target along the line of sight when it is at the initial position, the observed frequency will be the same as the emitted frequency, which is 5 GHz.