Upon the filing of a petition with the board of supervisors as outlined above, it shall be the duty of said board to fix a time and place for a public hearing upon the question of the public convenience and necessity for the creation of the proposed authority. The date fixed for such hearing shall be not more than thirty days after the filing of the petition, and the date of the hearing, the place at which it shall be held, and the purpose of the hearing shall be set forth in a notice to be signed by the clerk of the board of said county. Said notice shall be published in a newspaper having general circulation within such county once a week for at least three consecutive weeks prior to the date of such hearing. The first such publication shall be made not less than twenty-one days prior to the date of such hearing, and the last such publication shall be made not more than seven days prior to the date of such hearing.