Monetary policy takes medium run time to take effect. Why study it in short run? Well I'm reading a book on the IS-LM model. 
At the end of the chapter, page 125 in my edition, the author presents one paper showing some graphs where the monetary policy (monetary contraction - increasing 1% of the federal funds rate) influencing output, but with its greatest impact only being felt after 4 quarters, and continues well into the 8th quarter.
At the same time, when the impact of the monetary policy is the greatest, is when the price level also begins to noticeably change.

According to the author, since in the IS-LM model we've assumed that the price level is given, the fact that the price level only begins changes at 4th quarter, is a good support for our assumption. 

Well, my question then is, why should we study the monetary policy as if it had the same time to impact as fiscal policy in the short-run, when the graphs support more the medium-run impact? Or is it a matter of magnitude of the policy at hand?(The Central Bank can move the interest rate with a lot more leeway than just a 1%)
In an IS-LM model, expansionary monetary policy increases output and decreases the interest rate. Expansionary fiscal policy increases output and increases the interest rate, so the two types of policies are not equivalent.

Furthermore, monetary policy does not work in the long-run. See an AS-AD model for more details on that. The only reason monetary policy actually works, is because of the fixed prices and their slowly changing (increase) in the medium run. Otherwise inflation would rise immediately in response thereby making monetary policy not have any effect on real GDP.

To really get to the medium run you have to understand the short run first. Effects observed in the actual economy often are not as quick as in our models and take time. I wouldn't consider 4-8 quarters the medium run.

Hope this helps.