Chapter 33, Problem 69P

A source emitting light with frequency f moves toward you at speed u. By considering both time dilation and the effect of wavefronts “piling up“ as shown in Fig. 14.33, show that you measure a Doppler-shifted frequency given by

$f^{\prime }=f\sqrt{\frac{c+u}{c-u}}$

Use the binomial approximation (Appendix A) to show that this result can be written in the form of Equation 14.15 when u ≪ c.