Doppler
Wednesday 5th December
So, yesterday we were discussing when it’ll still be light before we leave work again - the conclusion being that it just about looks like it should be light just as the clocks change… so it’ll be the monday after clock-change day.
But that led on to other discussions culminating in the question: How fast do you have to approach a red traffic light for the doppler effect to make it appear green?
After a few sums, I came up with the following results…
To make red look green, assuming a red wavelength of 685nm and green wavelength of 532nm, you need to approach at 28.8% of the speed of light - that’s 192 million miles per hour.
Note that at that speed you could reach the sun from the earth in just 29 minutes.
If you have a less powerful car and can’t quite manage that one, it’s a lot easier to make a green light look red - by travelling away from it at just 22.3% of the speed of light… a mere 148 million miles per hour.
The real bonus is that if the red light camera catches you going through the light, and you’re driving a yellow car, it’ll look purple and they’ll never be able to find you.
so whats the stopping distance if you are travelling at 192 million miles per hour?
Mr H
5 Dec 07 at 11:19 am
According to my calculations, we’re talking around 350,000,000,000 miles in a standard car with good brakes in good conditions. In the wet it could be up to 700,000,000,000 miles.
The thinking distance is an insignificant 36,000 miles.
stu
5 Dec 07 at 11:31 am
Ok, So the Circumfrence of the Earth being about 24,900 miles.
So if you are travelling at 192 million miles per hour, and someone was to step out in front of you. You would run them over twice whilst in the ‘thinking distance’ followed by a further 14,056,224 times whilst braking in your standard car with good brakes.
Mr H
5 Dec 07 at 11:47 am
I think that speed may be sufficient to escape the earth’s gravitational pull, so you’d actually only run them over once.
Yes… the escape velocity of earth is only 25,200 mph.
stu
5 Dec 07 at 11:51 am
You could have magnetic wheels of some sort to keep you on the surface.
rich
5 Dec 07 at 1:10 pm
Ooh… good thought, rich.
stu
5 Dec 07 at 2:01 pm
Well I suppose once is enough for anyone.
But Michelin boast that their tyres stick to the road like glue, so if you escape the earth gravity, then you’ve got a case against them..
Mr H
5 Dec 07 at 2:30 pm
Ah, well… how fast would you have to travel away from a flute for the doppler shift to end up making it sound like a tuba?
DoGGa
5 Dec 07 at 3:03 pm
Well, DoGGa, it’d be less than the speed of sound, so eminently doable.
stu
5 Dec 07 at 3:15 pm
Alex in the office points out that the observer’s time is not the same as the driver’s time, have you allowed for that in your thinking time calculation?
sweavo
5 Dec 07 at 6:15 pm
So if you go from 186million mph to zero, assuming that its a steady drop, your average speed will be 92million MPH. Given that the stopping distance is 350,000,000,000 that means the time to stop your car will be 4069hours or just over 24 weeks.
Mr H
6 Dec 07 at 9:09 am
Fortunately, sweavo, Alex is in your office, not mine, so I can safely ignore him
Ooh… good calculating, Mr. H. 24 weeks, eh?
stu
6 Dec 07 at 9:25 am