Wave Speed on a String

When a wave travels on a string, the wave speed depends on both the string tension  and the mass per unit length μ, or linear mass density. What must the exact formula be? ( is now tension, not torque) Well the units of v are m sec^-1 and units of  are N ≡ kg m sec^-1 and units of μ are kg m^-1. To get m sec^-1 from kg m sec^-2 and kg m^-1 can only be obtained with

Thus we must have

And we can combine with our previous formula, so that the wave speed on a string is .