Morphing is more usually found in animation, video and photography, where software enables one image to morph with another. In digital audio, a morph is a more sophisticated version of a cross-fade, in which the content of the two soundfiles is actually intermingled during the intermediate stage. This project, however, concentrates on the perceptual, rather than the technical aspects of a sound morph.
Take two recorded sounds, such as a hi-hat hit and a snare drum. Using any available tools (pitch shifting, time stretching, etc) operate on one of the sound files only until it sounds as nearly as possible like the other. This may involve repeating the sound numerous times. Then do the same with the other sound file.
This is a fairly laborious exercise, and morphing software can perform what would be probably a more effective and smoother morph between the two files readily enough without all the effort. So why undertake the task? Because the aural awareness and understanding of the acoustic content of the sound it will produce will be invaluable. There will also be a spin-off benefit in understanding the timebased processes. Ask the following questions: is there an obvious point in time at which the character of the sound changes? Can this point be moved? Is the point the same for other people?