What is the period of a wave with the wave speed of 12m/s and a frequency of 60 hz?

To determine the period of a wave you need not utilize the value for the wave speed. 

The formula for the period is T= 1/f
T stands for period/time while f is for frequency. Substitute the value for the frequency which is 60 Hz. That would give you:

T= 1/60 Hz

convert Hz to cycles per second to extract the unit of time (s).

60 Hz x 1/s/1 Hz=  60/s

To continue the computation:

T=1/60/s that will give you a T= 0.017 s or 17 ms.