Understanding Radar Guns and Speed Measurement with STR

[O Great One]

Hello everyone,
I was just thinking about something...A police radar gun measures the speed of an object by the change in frequency of the reflected wave. For example...we might have a gun sending out a series of radio waves towards an object moving toward us like this...

GUN: )____)____)____)____)____)____)______<-object<-

in which case we would receive the following series of waves since each wave reaches the object more quickly:

GUN: (_(_(_(_(_(_(_______<-object<-

however, it seems that there should be no Doppler shift if the speed of light were constant. The waves should hit the object at the same rate, no matter what the speed of the object.

 

[pervect]

What makes you think there should be no doppler shift? It turns out that the formula for doppler shift is a function only of relative velocity. As stated at

http://scienceworld.wolfram.com/physics/DopplerEffect.html

relativistic doppler shift = sqrt((c+v)/(c-v))

 

[O Great One]

If I have a stream of cars passing me at a rate of 1 per second and their speed relative to me is to remain constant then they would have to continue passing me at a rate of 1 per second, no matter what my speed is. But, this doesn't happen in the case of the radar gun. The electromagnetic waves hit the object more or less frequently depending on the speed of the object.

 

[Doc Al]

If I have a stream of cars passing me at a rate of 1 per second and their speed relative to me is to remain constant then they would have to continue passing me at a rate of 1 per second, no matter what my speed is.

Well, that's true but not analogous to the radar gun scenario. A closer, albeit bizarre, analogy would be: A stream of cars pass you at the frequency of 1 per second, but then get reflected off of a moving wall which is approaching you. The frequency at which the reflected cars pass you by is greater than 1 per second, even though the speed at which the cars pass you is constant. (The distance between the cars is shorter in the reflected stream.)

 

[O Great One]

A stream of cars pass you at the frequency of 1 per second, but then get reflected off of a moving wall which is approaching you. The frequency at which the reflected cars pass you by is greater than 1 per second, even though the speed at which the cars pass you is constant. (The distance between the cars is shorter in the reflected stream.)

In your analogy, we're talking about the moving wall, which is the object, not about me, which would be the radar gun. So, yes, the cars would be reflected to me (the gun) at the same rate, but they would be faster relative to the moving wall (the object).

 

[Doc Al]

In your analogy, we're talking about the moving wall, which is the object, not about me, which would be the radar gun. So, yes, the cars would be reflected to me (the gun) at the same rate, but they would be faster relative to the moving wall (the object).

Not true. The speed of the (relativistic) cars with respect to the gun would be "c" according to the observer holding the gun, and it would also be "c" with respect to the wall according to observers moving with the wall.

 

[O Great One]

Somebody is throwing balls at me at a constant speed and frequency while I'm standing still. I'm holding a reflective shield which reflects the balls back towards the thrower at the same speed they were coming towards me. I start walking towards the thrower. I can state two things with certainty.

1. The speed of the balls relative to me will be faster once I start walking towards the thrower.

2. The thrower will receive the balls with greater frequency than when he threw them.

So, why doesn't the same logic apply to light?

 

[Doc Al]

1. The speed of the balls relative to me will be faster once I start walking towards the thrower.

This is certainly true for things (balls) moving at speeds less that the speed of light. But it doesn't apply to light. No matter how fast you move towards the light, its speed with respect to you remains constant. This is not common sense! But it is true and its consequences led to the development of special relativity.

2. The thrower will receive the balls with greater frequency than when he threw them.

This is true. The frequency will change for both balls and light. (But the speed of light will remain constant.)

So, why doesn't the same logic apply to light?

The common sense "logic" that tells you if the balls and you both move at speed "v" (with respect to the ground) then the speed of the balls with respect to you must be "v + v" is really a physical assumption of how the world works called galilean relativity. It's just not true, but is a good approximation for low speeds. For objects moving at high speeds (like light itself) that assumption is no good at all and must be replaced by special relativity.

 

[pervect]

Consider two objects, both emitting flashes at one per second.

The first object is stationary, the second object is moving towards you.

The stationary object will emit a flash, there will be a constant time delay of distance/c, and the flash will arive. Thus the interval that you'll see flashes is once per second.

THe moving object will emit a flash, and there will be a variable time delay of distance = (initial distance - velocity*time)/c. Because of the variable time delay, pulses will not arrive at once per second.