Measuring Speed with Doppler Effect: Questions and Challenges

  • #1
Stephanus
1,316
104
Dear PF Forum,
I'd like to know how to measure speed only by doppler effect.
Nugatory said:
[..]Now we have several ways of measuring speed. We can bounce a signal of known frequency (say [..]) and Doppler will tell us the speed. Or we can position two detectors at rest relative to us in its path at a known distance apart, have each detector send a flash of light our way as the object passes, and then by subtracting out the light travel times we have the time difference and so can calculate the speed using ##v=\Delta{x}/\Delta{t}##.[..]
What if we don't know the frequency?
What if we don't know the distance?
ST-02.jpg

If we look this diagram on our computer screen, we'll know everything. Distance, speed, time dilation event relative simultaneity of event. But here, there are no relative simultaneity of events, because they are all time like.
Here, Green (G) will send a signal to Blue (B) everytime G receives B signal.
And B can't rely on the frequency of G signal, it might, it might not be same. For example B signal is at 100 MHz, and G send its own signal regardless what B sends, say 50MHz.
And this is all that B can see:
B sends its clock time then, G sends back B's clock time.
Code:
Events Time A Diff   Freq  Read B
E1        700  ..       1   -1100   
E2        900  200  1 > 4    -900   
E3        950   50      4    -700   
E4       1125   …               0   
E5       1175   50      4     200
B can work out the speed by this formula
##f = \frac{1+V}{1-V}; 4 = \frac{1+V}{1-V}; V=\frac{3}{5}##
Time A column is B's clock when Blue receives the signal.
Read B column is the clock when Blue sent the signal.
Ok, it makes sense. Once the light cone from G entering B world line, the frequency changes to 4, forever.
Here at E2, actually Blue doesn't have to wait until E3, to know that the frequency changes. Blue could have sends signal at 1 pico seconds interval instead of 200 seconds interval. So right after E2, Blue can already detect the changing frequencey.

But I see something strange with this diagram.
ST-01.jpg

Here is what B reads from the signal from G

Code:
Events Time A    Diff      Freq   Read B
E1       -200      …          1    -2000
E2          0     200    1 -> 2    -1800
E3        100     100         2    -1600
E4        900      …                   0
E5        950      50         4      200
The instant Blue moves the frequency changes to 2.
After sometime the signal from the time when B moves is received by B, the frequency changes to 4.
So, there are times between (E2 and E4) when Blue miscalculates the speed if using the same method as above picture.
E4 is the event when B receives the bounce back signal from when B started to move.
When F = 2, V is 1/3
When F = 4, V is 3/5
Where did I go wrong?

Thanks.
 
Last edited:
Physics news on Phys.org
  • #2
Stephanus said:
Dear PF Forum,
I'd like to know how to measure speed only by doppler effect.

What if we don't know the frequency?
What if we don't know the distance?

The speed can be calculated by using a spectrometer to measure the change in the frequency of the light/radar pulse that is sent.

The distance to the reflection event can be found by timing the light/radar pulse.

So if blue has a radar gun that measures the Doppler the distance and speed can be got from a single pulse.
 

Attachments

  • dop-dist11.png
    dop-dist11.png
    2.1 KB · Views: 452
  • #3
Mentz114 said:
The speed can be calculated by using a spectrometer to measure the change in the frequency of the light/radar pulse that is sent.

The distance to the reflection event can be found by timing the light/radar pulse.
But, could you please take a look at diagram 2? Because the change of frequency is not consistent.
 
  • #4
Stephanus said:
But, could you please take a look at diagram 2? Because the change of frequency is not consistent.

Blue starts moving at t=0 so naturally the freqency changes.
 
  • #5
Mentz114 said:
Blue starts moving at t=0 so naturally the freqency changes.
And naturally Blue mistakenly calculate the speed until t=900, where the signal from Blue when starts move is received.
 
  • #6
Stephanus said:
And naturally Blue mistakenly calculate the speed until t=900, where the signal from Blue when starts move is received.
If the receiver or sender accelerates during the measurement then the process won't work.

Why are you making difficulties ? What don't you understand ?
 
  • Like
Likes Stephanus
  • #7
Mentz114 said:
If the receiver or sender accelerates during the measurement then the process won't work.

Why are you making difficulties ? What don't you understand ?
I understand now.
 
  • #8
No wait,
I think we should correct it
Mentz114 said:
If the receiver or sender accelerates during the measurement then the process won't work.

Why are you making difficulties ? What don't you understand ?
 
  • #9
Stephanus said:
No wait,
I think we should correct it
No. Doppler is reciprocal. If the relative velocity is not constant the formula does not apply as it stands.
 
  • Like
Likes Stephanus
  • #10
Mentz114 said:
No. Doppler is reciprocal. If the relative velocity is not constant the formula does not apply as it stands.
It really clears the path for me. Thanks.
 

Similar threads

Replies
5
Views
2K
Replies
114
Views
9K
Replies
31
Views
2K
Replies
30
Views
3K
Replies
6
Views
1K
Replies
7
Views
1K
Back
Top