A small source of sound travels on a circle as shown in the figure,...

According to the Doppler effect, the apparent frequency increases when the source approaches the observer and decreases when it recedes.

From the given figure, the arrow on the circular path indicates that the source is moving in a clockwise direction.

At point $B$, the velocity of the source is directed towards the observer at $O$. Since the source is approaching the observer, the apparent frequency $\nu_2$ is greater than the actual frequency $\nu_0$ ($\nu_2 > \nu_0$).

At point $A$, the velocity of the source is directed away from the observer at $O$. Since the source is receding, the apparent frequency $\nu_1$ is less than the actual frequency $\nu_0$ ($\nu_1 < \nu_0$).

At point $C$, the velocity of the source is perpendicular to the line of sight $CO$. Since there is no component of velocity along the line joining the source and the observer, there is no Doppler shift. The apparent frequency $\nu_3$ is equal to the actual frequency $\nu_0$ ($\nu_3 = \nu_0$).

Combining these observations, we get $\nu_2 > \nu_3 > \nu_1$.