Is there a change in frequency of sound for an observer at the center of a circle for a sound source moving in the circle?

I do not know why a circle would be relevant. Explain?

the point is since the velocity of sound is varying even though the distance between the source and the observer is unchanging I think there may be sth going on since the conditional is differnt from the classical way.

I try to imagine how the wavelength can change or not but can't follow it intuitively

Doppler effect only occurs if the distance between sound source and listener is changing.

That couldn't be an answer? doppler effect is all about whether there is change in frequency due to the apparent movement of source or observer or both.

I just want sth how to look at the problem.

"The Doppler effect (or Doppler shift), named after the Austrian physicist Christian Doppler, who proposed it in 1842 in Prague, is the change in frequency of a wave (or other periodic event) for an observer moving relative to its source. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession." From the Wikipedia page on Doppler Effect.

 

Note: higher frequency during approach (distance changing), and lower during recession (also distance changing).

The relative distance between them does not change, therefore there is no doppler effect, though if the person rotates on the spot at the rate of the rotation of the source it will eliminate all errors from the experiment. NB Any breeze will cause errors.