Consider a source of sound such as a person speaking or a party of people which makes a continual drone sound of the the same frequency. If a human shakes their head side-to-side with sufficient angular speed, they are in effect obtaining different frequencies of the same sound source and should be able to apply the Doppler effect to approximately localize (from prior experience) the sound source.
Do humans use the Doppler effect to localize sources of sound and have there been any studies proving this?
Edit: A link to the Weber-Fechner law and a link to the wiki article discussing the just-noticable-difference (JND) for music applications were added to the OP for reference, based on the accepted answer.
Best Answer
A person would not be able to localize a sound using the Doppler effect created by shaking their head.
Say a person shakes their head at 20 cm/s. The speed of sound is about 330 m/s. This gives a frequency change of 0.06%.
The "just noticeable difference" to discern two frequencies played in succession is about 0.6% (source), so about an order of magnitude too coarse.