Wing wobbles are used as a flirtation. Come Hither. There are several usages.
When a baby is hungry it will wobble one or both wings.
When a baby sees anyone or dove that might be a source of food, it might wobble its wings.
When a female adult is billing with her mate she may very vigorously wobble her wings like a baby feeding.
When a female is in the nest and wants attention from her mate, usually to bring her nest materials, she may wobble one wing very flirtatiously.
Wing flicking is different from a wing wobble so it is not included in this section.
The audio portions are described in the appropriate sections associated with the usage.
The hungry baby will sometimes wobble its wings so vigorously, it may actually attempt to wrap its wing around the parent to pull them down so it can reach their mouth to feed. The baby will also wobble its wings at anyone or any dove that it sees as a possible source for food including other babies.
The female wobbling her wings while billing may become as vigorous and aggressive with the wing wobbles as the hungry baby. Billing actually mimics being fed and in fact some food occasionally is passed from the male to the female during billing.
At any time that only one wing is wobbled, it is a flirtation or a come hither. Most often to get attention from the mate or the parent or even a stranger when the baby is hungry.