Doppler shift with microwaves i think

In summary, microwaves are reflected from an approaching airplane and when combined with the waves from the source, a beat frequency of 969 Hz is produced. Using the Doppler effect equation for light, it is found that the approach speed of the airplane is approximately 523.26 km/h.
  • #1
Dorbo
5
0
Doppler shift with microwaves...i think...

Homework Statement


Microwaves, which travel at the speed of light, are reflected from a distant airplane approaching the microwave source. It is found that when the reflected waves are beat against the waves radiating from the source, the beat frequency is given by 969 Hz. If the source microwaves are 150 mm in wavelength, what is the approach speed (in km/h) of the airplane?

Homework Equations


I think that the 3 relevant equations are [tex]C=\lambda[/tex] [tex]\nu[/tex]
and dopplers equation

[tex]F= \left(v+v_{r}\right)/\left(v+v_{s}\right)*F_{0}[/tex]

[tex]F_{beat} = \left|F_1-F_2\right|[/tex]

The Attempt at a Solution


My attempt at the solution is to take the speed of light, divide by .150 m, to get the frequency of my microwave. This value gives me [tex]\nu =1.998*10^9[/tex].
I then put it into the beat formula and solve for [tex]F_1= 1.997*10^9[/tex].
I would then sub into my dopplers formula, except i don't know if the source is moving towards it or if it is moving away. I am also not sure if i did any of this right because the microwave frequency is so high, that the beats have virtually no affect. Any insight would be appreciated, thank you in advance.
 
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  • #2


Hi Dorbo, welcome to PH.
In the case of light, the Doppler effect is given by
Δf/f = v*cosθ/C.
 
  • #3


rl.bhat said:
Hi Dorbo, welcome to PH.
In the case of light, the Doppler effect is given by
Δf/f = v*cosθ/C.

I am sorry, what is [tex]\Delta f[/tex] in your equation? And how do beats fit into it? From what i understand [tex]\theta = \pi[/tex] because the waves are going in opposite directions. I do understand what C is though :p.
 
  • #4


Dorbo said:
I am sorry, what is [tex]\Delta f[/tex] in your equation? And how do beats fit into it? From what i understand [tex]\theta = \pi[/tex] because the waves are going in opposite directions. I do understand what C is though :p.
Δf is the beat frequency.
The airplane is approaching. So the source appears to be coming towards the observer. Hence θ = 0.
 
  • #5


rl.bhat said:
Δf is the beat frequency.
The airplane is approaching. So the source appears to be coming towards the observer. Hence θ = 0.

Ok i put in [tex]\frac{969*C}{2*10^9}[/tex], i then got a value of 145.35 m/s, i then converted it to 523.26 km/h. I then submitted this answer and got it wrong. Any ideas, and thank you for the help so far. I got the 2*10^9 by [tex] c= \lambda \nu[/tex]
 
  • #6


Δf/f = v*cosθ/C.
This formula is for a source approaching the stationary observer.
In this case, when the reflector moves x meter per second with respect to the source, the image of the source in the reflector approaches the source with 2x meter per second. So try the answer 2*523.26 km/h.
 

1. What is Doppler shift with microwaves?

Doppler shift with microwaves is a phenomenon that occurs when the frequency of a microwave signal changes due to the relative motion between the source of the signal and the observer.

2. How does Doppler shift with microwaves work?

Doppler shift with microwaves works by measuring the change in frequency of the microwave signal as it is reflected off of a moving object. This change in frequency is then used to calculate the speed and direction of the object's movement.

3. What is the purpose of using Doppler shift with microwaves?

The main purpose of using Doppler shift with microwaves is for remote sensing and monitoring applications, such as weather radar and satellite measurements. It can also be used in navigation systems, such as GPS, to determine the speed and direction of an object.

4. What factors affect the accuracy of Doppler shift with microwaves?

The accuracy of Doppler shift with microwaves can be affected by various factors, including the speed and direction of the moving object, the frequency and power of the microwave signal, and any interference or noise in the environment.

5. Are there any limitations to using Doppler shift with microwaves?

Yes, there are some limitations to using Doppler shift with microwaves. It may not work well in certain weather conditions, such as heavy rain or fog, and it may also be affected by the shape and size of the object being measured. Additionally, it may not be as accurate when measuring objects that are moving at extremely high speeds.

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