Yes, we can apply doppler effect in such a case.
The apparent change in frequency of sound produced by a source heard by the observer whenever there is a relative motion between source and listener is called doppler effect.
When both source and observer are in the same circular path, well imagine a circular stadium ground (r=500m) and an advertisement vehicle with loudspeaker is moving around the circular path, and you are also walking in the same circular path,
CASE 1
If both your’s and the vehicle’s speed is same then yo don’t feel any change in the frequency of the sound from the loudspeaker. Hence no doppler effect
CASE 2
If the vehicle is moving faster from you(overtaking you) then you feel as if the noise from the loudspeaker have decreased. Here you felt a decrease in frequency. So you can apply doppler effect
CASE 3
You are walking and the vehicle is coming from behind you, as it comes closer don’t you feel as if the sound from the loudspeaker has increased?Here you felt the frequency increased. So you can apply doppler effect here.
CASE 4
You are staying in the middle of the circular path(at centre) and the vehicle is moving around you. Then you will not feel a change in frequency as the distance between you and vehicle is constant throughout and the sound reaches you with same frequency all around. Hence no doppler effect.
Hence whenever you feel there is a frequency change(change in the sound that reaches) between the source and listener there you can apply doppler effect of sound.
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Hope it was helpful and sorry that the explanation was too lengthy, I’m new at this.Please ask doubt if any. And more questions are welcome. Please approve ^_^