Answer
The period is halved. It is constant for a constant relative speed, but changes if there is accelerated motion.
Work Step by Step
Frequency and period are reciprocals of each other. If the frequency is doubled, the period is halved.
This is discussed on page 669, and shown in Figure 35.15.
For uniform motion, this situation is static, and the frequency and period do not change with time.
For accelerated motion, they do change. For example, if the approaching source moves faster and faster, each subsequent flash is emitted at a closer distance than the previous one. The frequency increases over time, and the period decreases with time.
