- 29 Feb '08 06:26 / 1 editI was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler shift that made the light look green to me; after all, I was approaching it. So he waived the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?
- 29 Feb '08 07:23

Ok, it appeared 520nm, or 0.00000052m*Originally posted by Jirakon***I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler ...[text shortened]... d the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?**

Speed of light = 299792458

V=Flamda

299792458=0.00000052F

F=576523957692308 Hz

Now it was actually 650nm, or 0.00000065m

So V = 576523957692308 x 0.00000065

Where V is the speed of light, plus the speed of your car.

V = 374740572.5

374740572.5 - speed of light = 74 948 114.5

So you were travelling at 74948114.5meters/second

= 208189.207meters/hour

= 129.362776mph

so you were travelling at 129mph.

Great question. - 29 Feb '08 07:45

Too fast wayyyyy too fast..... Haven't done one of these since school....*Originally posted by Jirakon***I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler ...[text shortened]... d the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?**

using W as wavelength since I don't have a lambda and /\ since I don't have delta

f' = f + f(v)/c

f = c/W

c/W' = c/W + (cv/w)/c

W'= W + v/Wc

/\W (c) = v (W) i think, could be wrong.....

/\W(c)/W = v

1.2X10^-7(3X10^8)/6.5X10^-7 = v (All in Meters per second)

V = 1.24 X 10^8 MPH

Too fast........

Please correct if this is wrong.... As I said its been a long time since physics at uni and this is all from memory.... - 29 Feb '08 07:47

Dammnit you got there first but....*Originally posted by doodinthemood***Ok, it appeared 520nm, or 0.00000052m**

Speed of light = 299792458

V=Flamda

299792458=0.00000052F

F=576523957692308 Hz

Now it was actually 650nm, or 0.00000065m

So V = 576523957692308 x 0.00000065

Where V is the speed of light, plus the speed of your car.

V = 374740572.5

374740572.5 - speed of light = 74 948 114.5

So you were travelling at ...[text shortened]... = 208189.207meters/hour

= 129.362776mph

so you were travelling at 129mph.

Great question.

Has to be faster surely? I've done 129 mph and not see a green light where once there was a red one?

Well I haven't but you get the point..... - 29 Feb '08 09:32

i think you did something wrong with the dimensional analysis... 1 meter/sec is appx 2.2 mph*Originally posted by doodinthemood***Ok, it appeared 520nm, or 0.00000052m**

Speed of light = 299792458

V=Flamda

299792458=0.00000052F

F=576523957692308 Hz

Now it was actually 650nm, or 0.00000065m

So V = 576523957692308 x 0.00000065

Where V is the speed of light, plus the speed of your car.

V = 374740572.5

374740572.5 - speed of light = 74 948 114.5

So you were travelling at ...[text shortened]... = 208189.207meters/hour

= 129.362776mph

so you were travelling at 129mph.

Great question.

so in very rough numbers it should be more than double the number of meters/second - i.e. 1.5 x 10^8 miles per hour... using google to convert, it gave me 167654157 mph which is about right

i think in going from seconds to hours you divided by 3600 where you should have multiplied - this gets it back to the correct magnitude of answers and damn i wish i could drive that fast. - 29 Feb '08 09:34

129 mph on a road with traffic lights?*Originally posted by Mexico***Dammnit you got there first but....**

Has to be faster surely? I've done 129 mph and not see a green light where once there was a red one?

Well I haven't but you get the point.....

You should lose your drivers license, if you have any. - 29 Feb '08 11:43

129 mph is not very fast. In germany they don't have any speed limits on some parts of the Autobahn. When I was there, pressing the pedal, I didn't see any color shifts anywhere, the trees weren't blue, the sun stayed yellow.*Originally posted by doodinthemood***... so you were travelling at 129mph.**

Great question.

I think we should be talking about way far higher speeds here... - 29 Feb '08 13:08

haha... that's the best excuse I have ever seen*Originally posted by Jirakon***I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler ...[text shortened]... d the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?**

but you would have to be going REALLY fast to see a doppler shift of around 20%.

Galaxies with that amount of redshift have to be moving at relativistic speeds. - 02 Mar '08 18:28

"classicaly" the velocity (in units of c) of the wave should be v = (1 - 530/650) = 0.1846*Originally posted by Mexico***Yea I thought it couldn't be that low..... Can someone tell me if I was right..... I think it is but as I said its from memory so maybe not......**

relativistically we use the equation given by Jirakon in the previous post, and gives v=0.2013

In this velocity range, the relativistic effect exists , but it's not that significant. - 02 Mar '08 18:49 / 1 editTo find the "classical" Doppler Shift, imagine an indian on a horse, throwing arrows at you every few seconds, let's say 1 arrow per second (this is the frequency).

If the indian starts moving towards you, he'll keep firing 1 arrow per second, but you'll be shot more frequently.

The analogy with sound or other wave is evident. The wavelength of a wave would correspond to the distance between consecutive shots.

Let's calculate it.

We only need to know the speed of the arrow (v).

The distance that first arrow moved from the point it was fired until the second arrow is fired is v * t (t is time between shots, equal to 1/f )

But in this time, the indian moved a little too! How much? Simply v_indian * t ... easy!

So the distance between arrows is simply v * t - v_indian*t

In wave language, lambda_observed=(v_wave - v_source) * t

Now, t, is equal to lambda / v_wave.

So, lambda_observed = lambda * (v_wave - v_source) / v_wave

If you want frequencies, know that lambda = v_wave / f

For this problem , we have wavelenghts and v_wave = 1 (in units of c)

so,

lambda_observed / lambda = (1 - v_source)

v_source = 1 - lambda_observed / lambda - 02 Mar '08 18:57
*In this velocity range, the relativistic effect exists , but it's not that significant.*

Not significant? 124 million mph to 135 million mph? I would call an eight percent error pretty significant.

The answer is ~135 million mph.

I have a confession to make. This story is not true. (glad I got that off my chest) - 02 Mar '08 19:04

Well... for a speed limit of 80 mph (?) -*Originally posted by Jirakon**In this velocity range, the relativistic effect exists , but it's not that significant.*

Not significant? 124 million mph to 135 million mph? I would call an eight percent error pretty significant.

The answer is ~135 million mph.

I have a confession to make. This story is not true. (glad I got that off my chest)*who the hell uses mph...*- it's quite irrelevant

And the idea of the problem is to show that you would have to move at a speed comparable to the speed of the wave to see a wave change. - 07 Mar '08 02:02

If he was going that fast, he wouldn't have had TIME to get a ticket, 167 million mph is what, about 0.16C or so? In one second he would have been 30,000 miles away and trying to figure out how to get home*Originally posted by Jirakon**In this velocity range, the relativistic effect exists , but it's not that significant.*

Not significant? 124 million mph to 135 million mph? I would call an eight percent error pretty significant.

The answer is ~135 million mph.

I have a confession to make. This story is not true. (glad I got that off my chest)