If a speaker is a variable load (different impedance at different frequencies)how will a speaker respond on an amp where the watts double from 4 to 2 ohms vs one where the difference is negligible? (ex:alpine pdx) Lets assume the speaker is rated at 4 ohms.

 

you need to review Ohms law: V=IR Power = (V^2)/R

An amp is a voltage gain device. Assuming same voltage out for all frequencies, then just use the power equation.

The 2 vs 4 ohm power rating of an amp is the MAXIMUM output.

So yes, if a speaker's impedance varies with frequency, so will the power it draws and dissipates given the same voltage, regardless of the amp's 2 vs 4 ohm maximum rating.

So if a speakers impedance doubles, then its power draw will halve.

 

would the response curve change between the two?

 

Not unless you have reached the maximum output of the amp!