Does the observed frequency approach infinity or does it become negative?

[k-hursh]

I chose to write an essay on the "interesting" question I stumbled upon

For part of it I am trying to calculate the Doppler shift in light with the relative motion of C. I suppose in the effort to not drone on for days I will first limit it to small, more simple questions and later,if we happen down a long path, so be it :).

I used the Relativistic Doppler Shift Formula for trying to calculate/prove the blue shift. The value I came up with is -1.585... I was expecting to get a value of 1, which would have indicated a forward, relative motion of one hundred percent the speed of light? So does anyone know if The Relative Doppler Shift is capable of being accurate when using the speed of light for relative motion/velocity? If so than is my math incorrect?

 

[malawi_glenn]

What formulas did you consider?

The Relative Doppler Shift is capable of being accurate when using the speed of light for relative motion/velocity?

$f = f' \sqrt{ \dfrac{c-v}{c+v}}$ where v is taken to be positive if the source is moving linearly awayfrom you, f is observed frequency and f' is frequency emitted. As you can see, when v approaces c, the observed frequency goes to 0, that is usually said as "red shifted to infinity".

Now, can you figure out what will happen if source is approaching, and if approaching in the limit v -> c?