How to Calculate the Speed of a Moving Object Using Radar and Beat Frequency?

In summary, the radar device emits microwaves with a frequency of 3.20e+09 Hz. When the waves are reflected from a van moving directly away from the emitter, the beat frequency between the source wave and the reflected wave is 838 beats per second. The van is first the observer then becomes the source and the frequency of the van is 78.56m/s.
  • #1
k77i
28
0

Homework Statement




A radar device emits microwaves with a frequency of 3.20e+09 Hz. When the waves are reflected from a van moving directly away from the emitter, the beat frequency between the source wave and the reflected wave is 838 beats per second. What is the speed of the van? (Note: microwaves, like all forms of electromagnetic radiation, propagate at the speed of light c = 3.00e+08 m/s.)


Homework Equations



frequency of beat = |f1-f2|

f' = [(v-vo)/v]fo
where v is the speed of emitted frequency (the speed of light on this case), vo is the speed of the observer and fo is the frequency of the observer
The above equation is for when the observer is moving away from the source and the source is stationary

The Attempt at a Solution



First i found the frequency of the observer (van) by using the first equation:

f(beat) = |f1-f2|
838 = |3.20e+09 - f2|
So f2 = 3 199 999 162

Then i used the second equation to find v0 (speed of the van):

f' = [(v-vo)/v]fo
3 199 999 162 = [(3.00e+08 - vo)3.00e+08]3.20e+09
this gave me vo = 78.56m/s, but according to the homework it's not right

Is it because I am not supposed to consider f2 as f'? If not I am not exactly sure how to solve for vo.
 
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  • #2
There are actually two doppler shifts here. Since these are radio waves I'm not sure if you can use the classical doppler equations (due to relativity).

The van is first a moving observer. The incident frequency is reflected at some frequency f'. You only know the incident frequency.

Now the van becomes a moving source of reflected microwaves (can you see why?) Apply the appropriate doppler equation using the f' from earlier as your incident frequency and 3 199 999 162 as your observed frequency.
 
  • #3
AtticusFinch said:
The van is first a moving observer. The incident frequency is reflected at some frequency f'. You only know the incident frequency.

Now the van becomes a moving source of reflected microwaves (can you see why?) Apply the appropriate doppler equation using the f' from earlier as your incident frequency and 3 199 999 162 as your observed frequency.

ok so i get why the van is first the observer then becomes the source.
so if i do it like that, I should set up the first equation as:

f' = [(v-vo)/v]fo = [(1 - vo/3.00*10^8)]3.2*10^9

Is this right? because then i still didn't find the f' from the first equation which you're telling me to use as the incident frequency (fo) in the second equation when the van is the source
 
  • #4
k77i said:
ok so i get why the van is first the observer then becomes the source.
so if i do it like that, I should set up the first equation as:

f' = [(v-vo)/v]fo = [(1 - vo/3.00*10^8)]3.2*10^9

Is this right? because then i still didn't find the f' from the first equation which you're telling me to use as the incident frequency (fo) in the second equation when the van is the source

If you're teacher wants you to ignore relativity you are correct so far.

Now, like you are saying, write another equation for the van as a moving source. The initial frequency is f' and the observed frequency is given as 3 199 999 162. If i remember correctly it should look like this:

3199999162=(v/(v+vs))f'

but you have already expressed f' in terms of vo which is equal to vs.

So through substitution you'll get a equation with only one unknown.
 
  • #5
AtticusFinch said:
If you're teacher wants you to ignore relativity you are correct so far.

Now, like you are saying, write another equation for the van as a moving source. The initial frequency is f' and the observed frequency is given as 3 199 999 162. If i remember correctly it should look like this:

3199999162=(v/(v+vs))f'

but you have already expressed f' in terms of vo which is equal to vs.

So through substitution you'll get a equation with only one unknown.

Alright then basically the final equation should look something like this?
3199999162 = ((9.6*10^17)/(3*10^8+x))-(9.6*10^17x)/(9.6*10^16+3*10^8x), where x is the value of the speed of the van.

Because this gives me 'no solution'
 
  • #6
k77i said:
Alright then basically the final equation should look something like this?
3199999162 = ((9.6*10^17)/(3*10^8+x))-(9.6*10^17x)/(9.6*10^16+3*10^8x), where x is the value of the speed of the van.

Because this gives me 'no solution'

Ok that's fine. Remember beats can mean the incident frequency is either lower than the emitted by 838 Hz or higher than the emitted by 838 Hz. You know the lower one didn't work so try the higher one.
 

1. What is the speed of sound waves?

The speed of sound waves depends on the medium through which they are traveling. In general, sound travels faster in solids than in liquids, and faster in liquids than in gases. The speed of sound in air at room temperature is approximately 343 meters per second.

2. How do you calculate the speed of a sound wave?

To calculate the speed of a sound wave, you need to know the frequency and wavelength of the wave. The speed of sound can be found by multiplying the frequency by the wavelength. This equation is represented as: speed = frequency x wavelength.

3. Why is the speed of sound important?

The speed of sound is important because it helps us understand how sound travels through different mediums and how we perceive sound. It also has practical applications, such as in the design of musical instruments and understanding the behavior of sound in different environments.

4. How does temperature affect the speed of sound?

The speed of sound is directly affected by temperature. As temperature increases, the speed of sound also increases. This is because sound travels faster through warmer air, which has more kinetic energy and is less dense. The opposite is true for colder temperatures.

5. Can the speed of sound be changed?

Yes, the speed of sound can be changed by altering the properties of the medium through which it travels. For example, the speed of sound can be increased by increasing the temperature or density of the medium. The speed of sound can also be changed by changing the frequency or wavelength of the sound wave.

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