Help with moving emitter/receiver cutoff speed

[ktoz]

Hi

I'm working on a Mac application to visually illustrate the doppler effect and managed to confuse myself with the following problem. I'm sure it's an easy one but I've been looking at it too long and can't figure it out.

Here's it is:

Given two objects moving at the same speed along parallel paths on a plane, and a signal (say little marbles) being shot between them, where the time it takes for the signal to go from one object to the other is one second. If you accelerate the objects, at what speed, relative to the signal speed, would a signal from object "A" never arrive at object "B"?

I tried drawing a circle from the center of object "A" through the center of object "B" and see from that, that if the objects are moving at the same speed as the signal, it would never arrive at "B" but the cutoff speed is some value less than one and I can't seem to figure it out.

Can anyone help me untangle this?

Thanks for any help

 

[tnich]

Hi

I'm working on a Mac application to visually illustrate the doppler effect and managed to confuse myself with the following problem. I'm sure it's an easy one but I've been looking at it too long and can't figure it out.

Here's it is:

Given two objects moving at the same speed along parallel paths on a plane, and a signal (say little marbles) being shot between them, where the time it takes for the signal to go from one object to the other is one second. If you accelerate the objects, at what speed, relative to the signal speed, would a signal from object "A" never arrive at object "B"?

I tried drawing a circle from the center of object "A" through the center of object "B" and see from that, that if the objects are moving at the same speed as the signal, it would never arrive at "B" but the cutoff speed is some value less than one and I can't seem to figure it out.

Can anyone help me untangle this?

Thanks for any help

I am not sure that I understand your question. I think you mean that you are using Newtonian physics and you are viewing the problem in some fixed reference frame. I think you are also assuming that the signal speed is a constant with respect to the reference frame, that is, changing the speed of object A with respect to the reference frame does not change the signal speed.

If that is the problem you are trying to solve, it seems to me that the limiting speed is the signal speed. At any object speed less than that, you can solve for the time at which the signal will reach the object B.

Perhaps you are uncomfortable with the idea that you can make object B's speed as close as you like to the signal speed and the signal can still intercept it, but when their speeds are equal no intercept is possible. But it seems to me that is just what you are looking for - the exact speed at which object B can no longer receive the signal.