Special Relativity: Rocket Signal Reception Time and Frequency Shift

[physiks]

Homework Statement

A rocket of proper length 100m travels at a speed 0.6c relative to a space station, which is on the rocket’s flight path.

I have so far had to work out that:
According to an observer on the space station, the nose of the rocket is a distance of 200m away from the station upon receiving the signal. This occurs at a time t=200/c, and that light of wavelength 500nm emitted from the station is observed at 1000nm in the rocket frame.

The space station continues to transmit signals every second (according to its own clock). At what time has the rocket received 500 signals as measured by its own clock? How many signals according to an observer on the space station have been transmitted during the corresponding time period?

Homework Equations

Length contraction, time dilation, relativistic doppler effect.

The Attempt at a Solution

I'm very confused about this, as it seems to be a simple doppler effect problem to me. I.e the 1 second time period translates to 2 seconds in the rocket frame, and then the rocket has received 500 signals after 1000s in its frame. However this isn't right...

 

[Simon Bridge]

according to the ship, the station clock runs slow.

 

[physiks]

according to the ship, the station clock runs slow.

In the station frame, a signal is emitted every t'=1s - this is a proper time. The lorentz factor γ=1.25 here. Therefore somebody on the spaceship sees the signals emitted every γt'=1.25s, i.e the time is dilated. Isn't this true?

 

[physiks]

Anybody?

 

[dauto]

This problem is overdetermined and inconsistent. The wavelength data is not consistent with the relative speed data. Try using the Relativistic Doppler effect formula.

 

[physiks]

This problem is overdetermined and inconsistent. The wavelength data is not consistent with the relative speed data. Try using the Relativistic Doppler effect formula.

Hmm those are previous parts to the question that I have already answered. How is the wavelength inconsistent with the speed data?

λ=λ'√(1+β)/√(1-β)
β=0.6
λ=2λ'
λ=2*500nm
λ=1000nm