Dimensional analysis is used to check the validity of an equation relating the speed of sound (v) in a gas to its pressure (P) and density ($\rho$). Which limitation prevents dimensional analysis from distinguishing between $v = \sqrt{P/\rho}$ and $v = \sqrt{14P/\rho}$?

If the formula for the velocity of a wave is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is tension and $\mu$ is mass per unit length. Using dimensional analysis, which aspect of this formula cannot be derived?