Suppose that a string of length L and mass m is under tension F.
(a) Show that (FL/m has units of speed.
(b) Show that there is no other combination of L, m, and F with units of speed. [Of the dimensions of the three quantities L, m, and F, only F includes time.] Thus, the speed of transverse waves on the string can only be some dimensionless constant times (FL/m.