Lets say that I have a spring... (we all know wave velocity is a function of the medium that the wave is passing through) Ok...I take this spring and stretch it very very far. The spring has a lot of tension. I create a pulse of X amplitude etc. with the tension up I would imagine that the wave velocity would be quick because the spring is tight...which makes the medium ideal for a high wave velocity. During this experiment I measure the time it takes the pulse to travel the entire spring.... I take this same spring and shorten it up making the tension less, setting the medium up for a slow wave velocity. This time when I make a wave of X amplitude etc, it will be slower than in the first trial. BUT the distance from one end of the spring to the other is less. Since we are dealing with the same spring just adjusting the tension....is the Time at which wave X gets from one end to the other of the spring going to be the same no matter how tightly the spring is stretched?