This is a dimensional analysis problem. Remember that the units on both sides of an equation must be the same. So all we need to do is count the number of units on each side and equate them.
Your equation is:
where L is distance, T is time, and M is mass.
This problem is strange. Technically I would say it can't be done, but I suppose there is an answer, however misleading the question is. Let me explain:
Matching the units on both sides we get that:
The solution is:
c = 0
b = 1/2
a = 1/2
So the relationship between the variables is:
My problem is that the question specifically stated that the wave speed depends on the density, which it doesn't according to the answer. I don't like questions that do this!