Which of the following can replace "the bark of the dog" to use a genitive case correctly?

Using "the dog's bark" utilizes the genitive case correctly by indicating possession. In this structure, "dog's" functions as a possessive noun, showing that the bark belongs to the dog. This form succinctly conveys the relationship between the two nouns, where "dog" modifies "bark" by illustrating ownership.

In contrast, the other options either do not appropriately convey possession or alter the meaning in ways that are not required. "The bark dog's" improperly positions 'bark' and 'dog' in a way that doesn't follow standard grammatical rules for possessive forms. "The barking dog" transforms the subject to emphasize action rather than possession, and "The dog barks" describes an action rather than identifying the possession of the bark. Thus, "the dog's bark" is the most suitable choice for expressing possession using a genitive case.