If you wanted to know the week number in a year, you'd just have to use WEEKNUM(serial_num,[return_type])

If you wanted to know the week number in a month, you could use the following formula

=IF(MONTH(A1)>1,WEEKNUM(A1,2)-WEEKNUM(DATE(YEAR(A1),MONTH(A1),0),2)+1,WEEKNUM(A1 ,2))

You could make it shorter with the EOMONTH formula as below

=IF(MONTH(A1)>1,WEEKNUM(A1,2)-WEEKNUM(EOMONTH(A1,-1),2)+1,WEEKNUM(A1,2))

For those who are inclined to the mathematics of it, you could use an even intuitive formula

=ROUNDUP((A1-EOMONTH(A1,-1))/7,0)