Problem with relativistic doppler?

[Piyu]

Homework Statement

Not really a homework, but i did run across it while attempting some questions. Was reading through the derivations of relativistic doppler effect on EM waves and was reading wiki(http://en.wikipedia.org/wiki/Relativistic_Doppler_effect" when i came across something.

Under the section of motion along the line of sight, they initially used the source frame as the reference frame yet later when they introduced time dilation into the picture, the observer becomes T_0 ? I always thought T_0 referred to the proper time in which case shouldn't it be the frame of the moving source?

b]2. Homework Equations [/b]

The Attempt at a Solution

I'm able to solve this using time dilation first before plugging in the non relativistic formula for doppler effect. However, this way seems to go against that method?

 

[Beaker87]

Wikipedia is starting in the reference frame of the source of the waves in order to find the time between successive crests hitting the moving observer in the reference frame of the source.Then Wikipedia uses this time in the time dilation equation in the observer's reference frame in order to find what this same time is in the reference frame of the observer.

 

[Piyu]

Yeah so how come time dilation uses the observer as the proper time. This is the same as if we put a clock on the source frame that ticks with every frequency and the observer sees it going faster than the source itself.

According to time dilation, should'nt the "tick" of each clock in the source frame be the proper time in this case?

 

[vela]

There are two events: reception by the observer of the two crests. In the source frame, the two events are separated by both space and time. In the observer's frame, the two events happen at the same point in space. So it's the observer who plays the role of the moving clock.