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Roller Coaster

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
Debbie is inside a roller coaster, which moves very quickly with a constant speed around a circle (parallel to the ground). She notices that during the motion she can hear the music played by the entertainment park, but the frequency varies considerably in different stages of the roller coaster's cycle.

In particular, she measures with her stopwatch that the maximum frequency pitch occurs every 4.02 seconds, and that the time interval between a maximum and a minimum pitch is 1.57 seconds.

When the ride finishes, she asks the security steward how large the roller coaster is, and he replies that its radius is 10.22 meters.

Can you calculate how far from the roller coaster's centre the speaker is? You might want to draw a diagram showing the circular roller coaster and the speaker, which you can assume that lies on the same horizontal plane as the roller coaster.