Building an ac electromagnet
I want to generate a sinusoidal electromagnetic field of a specificed frequency between 30-80 Hz....What do I generate an ac current of the specified frequency?


You need to buy a signal generator or build an oscillator. If it must be capable of generating any frequency in the specified range, it must have an adjustment that covers the range. An amplifier will likely be required to provide sufficient power to drive the coil.


  How do I make sure the magnetic core of the electromagnet does not saturate between 30-80 Hz...


The voltage must be adjustable to suit the frequency, winding and core design.


  The magnetic field just needs to be measurable from 1-3 meters by a magnetometer.


That seems to imply that the primary objective is to generate a magnetic field in air rather than an iron core. Perhaps you need a magnetic core with a 1 to 3 meter air gap. If you can not make the 1 to 3 meter space an air gap in a longer iron path for the field, I don't believe there is any benefit to using an iron core.

You need to first determine the strength of the magnetic field. If that is not specified for you, you must determine the sensitivity of the magnetometer that you can afford to purchase and then determine how to design a coil that will produce the field that you can detect.


  Do I need to worry about the electromagnet heating up because of this?


If you are going to use an iron core, you need to be concerned by heat generated in the iron by eddy currents and hysteresis. You also need to be concerned by heat generated in the wire by the flow of current. At a higher frequency, you would need to be concerned by skin-effect and eddy-current effects in the copper.

I believe that the question is too broad to allow a more specific answer.