Consider the derivation of the speed of a longitudinal wave. Instead of the bulk modulus B, the quantity of interest is the change in force per fractional length change. The force constant k' is the change in force per length change, so the force change per fractional length change is k' L, the applied force at one end is F = (k' L)(v y /v) and the longitudinal impulse when this force is applied for a time t is k' Ltv y /v. The change in longitudinal momentum is ((vt)m/L)v y and equating the expressions, canceling a factor of t and solving for v gives v 2 = L 2 k'/m.

An equivalent method is use, which relates the force constant k' and the "Young's modulus" of the Slinky, k' = YA/L, or Y = k'L/A. The mass density is ρ = m/(AL)

(2.00m) = 4.90 m/s