How can you change the speed of a vibrating rope by changing the mass on the rope?

Answer

The mass of a rope, in the context of vibrations, actually means the mass per unit length, for example kilograms per meter.

You can increase this specific mass by hanging any mass on the rope. The challenge is to add this added mass as continuously and evenly as possible. One possible way is to spirally twist another rope around it. This is a technique that is applied to stringed instruments (guitar, piano …). The thicker strings typically have a core wire, around which another wire is wound. The only reason for this is to increase the mass per unit length of the string so that it vibrates in the correct frequency range under an appropriate tension. Google the following keywords: wound strings

For your practical experiment it is theoretically possible to weight the rope in this way. It doesn’t seem easy to me, without the right tools and the necessary experience. I think just taking heavier rope is an interesting option. To know the mass of the rope, just put 1 meter of rope on the scale. If you want to weight the rope so that the waves propagate more slowly (under the same rope tension), you change the rope. That’s a much easier way to vary the mass parameter.