Suppose there is a speaker emitting a steadily changing frequency sound while moving counterclockwise in a circle with radius of $r=1 \space m$. There is an observer listening to a sound with the same frequency located 2 meters from the outside of the circle, as seen in the figure below:
The sound moves at a constant angular speed $\omega$.
You may assume the motion is slow enough that the Doppler Effect is insignificant, and that the speed of sound in air is 350 m/s.
The frequency of both speakers change together at a constant rate, such that the observer never hears a sound.
Which of the following could be an expression of the frequency as a function of time? Let $t=0$ be when $\theta=0$, i.e. when the speaker is at the opposite end of the circle relative to the observer.