There are some plastic corrugated tubes that are used to carry water away from the house (not the slotted type). These have a rectangle molded on one end to fit over the 3" or 4" downspout.
You can take the bottom elbooow off and screw a length of this corrugated plastic tubing to athe vertical section then run it away from the house. Should stop the noisy dripping on the aluminum elbow.
Something like this should cut the sound. Maybe attach it up higher and run it out at an angle if the first try at the bottom in not quiet enough.
Jim at Dawn