Relativistic doppler shift

[L_landau]

Homework Statement

A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of λ0=589 nm. Wavelength l is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift λ-λ0?

Homework Equations

Since the light source is always moving tangent to the center of the circle, I figured that I should use the doppler shift for transverse movement ƒ = ƒ₀√1-β².

The Attempt at a Solution

Using the above and solving for λ, Δλ = 2.95nm. Is this correct?

 

[TSny]

Looks right to me. (I get 2.97 nm for the shift.)