AL Physics - Doppler Effect

Suppose that the merry-go-round rotates with a constant angular speed, then the boy's velocity relavitve to the observer will be:
v = ωR sin ωt where R = radius of the merry-go-round and ω = angular velocity.
With the observer stationary, the apparent frequency will vary with time as:
f = fo[v/(v + ωR sin ωt)] where v is the sound velocity.
So among all choices, D will be a possible ans since it is NOT a sinusoidal nor reciprocal of sinusoidal variation.