The office or studio of a physician, painter, sculptor, surgeon, architect, dentist, teacher, musician, lawyer or engineer or similar professional occupation as may be interpreted by the Board of Zoning Appeals, residing in the dwelling unit in which such office or studio is located, provided there is no display or advertising on the premises in connection with such use except for a professional nameplate not over four square feet in area, provided that said name plate shall comply with the provisions of Article VI of this chapter, and provided, also, that such studio or office does not occupy more space than the equivalent of 1/4 of the area of one floor of such dwelling and that such use is merely incidental to the use of such dwelling unit primarily for residential purposes; provided, however, that any such musician's studio is equipped and used in such a manner that sounds therefrom are not unduly annoying to other persons on nearby premises or public places; and provided, further, that no assistants, whether paid or not, may participate in such use, except that one assistant may be employed if the nature of the profession is such as to require an assistant; and provided, further, that no use shall be made of more than one building in connection with such professional use; and provided, further, that such professional use shall not be deemed to include the right to engage in wholesale or retail trade, as such term is ordinarily understood. The Board of Zoning Appeals shall have power to determine what is a profession or occupation permitted under this subsection.