It is hard to take a stab at it without the question, but I will try because i was trained under extraordinary conditions 🙄
I am going to assume that we talking about velocity in a string
we have to consider two factors: (1) the pressure and (2) the density of the medium through which the wave travels. a good example is water , due to its density it slow the wave velocity but because it has a much higher pressure the velocity increases in comparing to air.
For the Spring (tension is like pressure in water) if the tension is higher then density of the spring then velocity is higher.